Fisher's One-Sample Randomization (Permutation) Test for Location

Perform Fisher's one-sample randomization (permutation) test for location.

oneSamplePermutationTest(x, alternative = "two.sided", mu = 0, exact = FALSE, 
    n.permutations = 5000, seed = NULL, ...)

Arguments

x: numeric vector of observations. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed.
alternative: character string indicating the kind of alternative hypothesis. The possible values are "two.sided" (the default), "less", and "greater".
mu: numeric scalar indicating the hypothesized value of the mean. The default value is mu=0.
exact: logical scalar indicating whether to perform the exact permutation test (i.e., enumerate all possible permutations) or simply sample from the permutation distribution. The default value is exact=FALSE.
n.permutations: integer indicating how many times to sample from the permutation distribution when exact=FALSE. The default value is n.permutations=5000. This argument is ignored when exact=TRUE.
seed: positive integer to pass to the R function set.seed. The default is seed=NULL, in which case the current value of .Random.seed is used. Using the seed argument lets you reproduce the exact same result if all other arguments stay the same.
...: arguments that can be supplied to the format function. This argument is used when creating the names attribute for the statistic component of the returned list (see permutationTest.object).

Details

Randomization Tests
In 1935, R.A. Fisher introduced the idea of a randomization test (Manly, 2007, p. 107; Efron and Tibshirani, 1993, Chapter 15), which is based on trying to answer the question: “Did the observed pattern happen by chance, or does the pattern indicate the null hypothesis is not true?” A randomization test works by simply enumerating all of the possible outcomes under the null hypothesis, then seeing where the observed outcome fits in. A randomization test is also called a permutation test, because it involves permuting the observations during the enumeration procedure (Manly, 2007, p. 3).

In the past, randomization tests have not been used as extensively as they are now because of the “large” computing resources needed to enumerate all of the possible outcomes, especially for large sample sizes. The advent of more powerful personal computers and software has allowed randomization tests to become much easier to perform. Depending on the sample size, however, it may still be too time consuming to enumerate all possible outcomes. In this case, the randomization test can still be performed by sampling from the randomization distribution, and comparing the observed outcome to this sampled permutation distribution.

Fisher's One-Sample Randomization Test for Location
Let $\underline{x} = x_1, x_2, \ldots, x_n$ be a vector of $n$ independent and identically distributed (i.i.d.) observations from some symmetric distribution with mean $\mu$. Consider the test of the null hypothesis that the mean $\mu$ is equal to some specified value $\mu_0$: $$H_0: \mu = \mu_0 \;\;\;\;\;\; (1)$$ The three possible alternative hypotheses are the upper one-sided alternative (alternative="greater") $$H_a: \mu > \mu_0 \;\;\;\;\;\; (2)$$ the lower one-sided alternative (alternative="less") $$H_a: \mu < \mu_0 \;\;\;\;\;\; (3)$$ and the two-sided alternative $$H_a: \mu \ne \mu_0 \;\;\;\;\;\; (4)$$ To perform the test of the null hypothesis (1) versus any of the three alternatives (2)-(4), Fisher proposed using the test statistic $$T = \sum_{i=1}^n y_i \;\;\;\;\;\; (5)$$ where $$y_i = x_i - \mu_0 \;\;\;\;\;\; (6)$$ (Manly, 2007, p. 112). The test assumes all of the observations come from the same distribution that is symmetric about the true population mean (hence the mean is the same as the median for this distribution). Under the null hypothesis, the $y_i$'s are equally likely to be positive or negative. Therefore, the permutation distribution of the test statistic $T$ consists of enumerating all possible ways of permuting the signs of the $y_i$'s and computing the resulting sums. For $n$ observations, there are $2^n$ possible permutations of the signs, because each observation can either be positive or negative.

For a one-sided upper alternative hypothesis (Equation (2)), the p-value is computed as the proportion of sums in the permutation distribution that are greater than or equal to the observed sum $T$. For a one-sided lower alternative hypothesis (Equation (3)), the p-value is computed as the proportion of sums in the permutation distribution that are less than or equal to the observed sum $T$. For a two-sided alternative hypothesis (Equation (4)), the p-value is computed by using the permutation distribution of the absolute value of $T$ (i.e., $|T|$) and computing the proportion of values in this permutation distribution that are greater than or equal to the observed value of $|T|$.

Confidence Intervals Based on Permutation Tests
Based on the relationship between hypothesis tests and confidence intervals, it is possible to construct a two-sided or one-sided $(1-\alpha)100\%$ confidence interval for the mean $\mu$ based on the one-sample permutation test by finding the values of $\mu_0$ that correspond to obtaining a p-value of $\alpha$ (Manly, 2007, pp. 18–20, 113). A confidence interval based on the bootstrap however, will yield a similar type of confidence interval (Efron and Tibshirani, 1993, p. 214); see the help file for boot in the R package boot.

Value

A list of class "permutationTest" containing the results of the hypothesis test. See the help file for permutationTest.object for details.

References

Efron, B., and R.J. Tibshirani. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York, pp.224–227.

Manly, B.F.J. (2007). Randomization, Bootstrap and Monte Carlo Methods in Biology. Third Edition. Chapman & Hall, New York, pp.112-113.

Millard, S.P., and N.K. Neerchal. (2001). Environmental Statistics with S-PLUS. CRC Press, Boca Raton, FL, pp.404–406.

Author

Steven P. Millard (EnvStats@ProbStatInfo.com)

Note

A frequent question in environmental statistics is “Is the concentration of chemical X greater than Y units?”. For example, in groundwater assessment (compliance) monitoring at hazardous and solid waste sites, the concentration of a chemical in the groundwater at a downgradient well must be compared to a groundwater protection standard (GWPS). If the concentration is “above” the GWPS, then the site enters corrective action monitoring. As another example, soil screening at a Superfund site involves comparing the concentration of a chemical in the soil with a pre-determined soil screening level (SSL). If the concentration is “above” the SSL, then further investigation and possible remedial action is required. Determining what it means for the chemical concentration to be “above” a GWPS or an SSL is a policy decision: the average of the distribution of the chemical concentration must be above the GWPS or SSL, or the median must be above the GWPS or SSL, or the 95'th percentile must be above the GWPS or SSL, or something else. Often, the first interpretation is used.

Hypothesis tests you can use to perform tests of location include: Student's t-test, Fisher's randomization test, the Wilcoxon signed rank test, Chen's modified t-test, the sign test, and a test based on a bootstrap confidence interval. For a discussion comparing the performance of these tests, see Millard and Neerchal (2001, pp.408-409).

Examples

  # Generate 10 observations from a logistic distribution with parameters 
  # location=7 and scale=2, and test the null hypothesis that the true mean 
  # is equal to 5 against the alternative that the true mean is greater than 5. 
  # Use the exact permutation distribution. 
  # (Note: the call to set.seed() allows you to reproduce this example).

  set.seed(23) 

  dat <- rlogis(10, location = 7, scale = 2) 

  test.list <- oneSamplePermutationTest(dat, mu = 5, 
    alternative = "greater", exact = TRUE) 

  # Print the results of the test 
  #------------------------------
  test.list 
#> $statistic
#> Sum(x - 5) 
#>   49.77294 
#> 
#> $parameters
#> NULL
#> 
#> $p.value
#> [1] 0.001953125
#> 
#> $estimate
#>     Mean 
#> 9.977294 
#> 
#> $null.value
#> Mean (Median) 
#>             5 
#> 
#> $alternative
#> [1] "greater"
#> 
#> $method
#> [1] "One-Sample Permutation Test\n                                 (Exact)"
#> 
#> $estimation.method
#> NULL
#> 
#> $sample.size
#>  n 
#> 10 
#> 
#> $data.name
#> [1] "dat"
#> 
#> $bad.obs
#> [1] 0
#> 
#> $stat.dist
#>    [1] -50.76433285 -45.52894718 -49.77294023 -44.53755456 -49.56281095
#>    [6] -44.32742528 -48.57141833 -43.33603266 -43.16871044 -37.93332477
#>   [11] -42.17731782 -36.94193215 -41.96718854 -36.73180287 -40.97579592
#>   [16] -35.74041025 -40.71385853 -35.47847286 -39.72246591 -34.48708024
#>   [21] -39.51233663 -34.27695096 -38.52094401 -33.28555834 -33.11823612
#>   [26] -27.88285045 -32.12684350 -26.89145783 -31.91671422 -26.68132855
#>   [31] -30.92532160 -25.68993593 -47.99440683 -42.75902117 -47.00301421
#>   [36] -41.76762855 -46.79288494 -41.55749927 -45.80149231 -40.56610665
#>   [41] -40.39878442 -35.16339876 -39.40739180 -34.17200614 -39.19726253
#>   [46] -33.96187686 -38.20586990 -32.97048424 -37.94393251 -32.70854685
#>   [51] -36.95253989 -31.71715423 -36.74241062 -31.50702495 -35.75101800
#>   [56] -30.51563233 -30.34831010 -25.11292444 -29.35691748 -24.12153182
#>   [61] -29.14678821 -23.91140254 -28.15539559 -22.92000992 -33.66622188
#>   [66] -28.43083622 -32.67482926 -27.43944360 -32.46469999 -27.22931432
#>   [71] -31.47330737 -26.23792170 -26.07059947 -20.83521381 -25.07920685
#>   [76] -19.84382119 -24.86907758 -19.63369191 -23.87768495 -18.64229929
#>   [81] -23.61574757 -18.38036190 -22.62435494 -17.38896928 -22.41422567
#>   [86] -17.17884000 -21.42283305 -16.18744738 -16.02012516 -10.78473949
#>   [91] -15.02873253  -9.79334687 -14.81860326  -9.58321759 -13.82721064
#>   [96]  -8.59182497 -30.89629587 -25.66091020 -29.90490325 -24.66951758
#>  [101] -29.69477397 -24.45938830 -28.70338135 -23.46799568 -23.30067346
#>  [106] -18.06528779 -22.30928084 -17.07389517 -22.09915156 -16.86376589
#>  [111] -21.10775894 -15.87237327 -20.84582155 -15.61043588 -19.85442893
#>  [116] -14.61904326 -19.64429965 -14.40891398 -18.65290703 -13.41752136
#>  [121] -13.25019914  -8.01481347 -12.25880652  -7.02342085 -12.04867724
#>  [126]  -6.81329157 -11.05728462  -5.82189895 -31.56214932 -26.32676365
#>  [131] -30.57075670 -25.33537103 -30.36062742 -25.12524175 -29.36923480
#>  [136] -24.13384913 -23.96652691 -18.73114124 -22.97513429 -17.73974862
#>  [141] -22.76500501 -17.52961934 -21.77361239 -16.53822672 -21.51167500
#>  [146] -16.27628933 -20.52028238 -15.28489671 -20.31015310 -15.07476743
#>  [151] -19.31876048 -14.08337481 -13.91605259  -8.68066692 -12.92465997
#>  [156]  -7.68927430 -12.71453069  -7.47914502 -11.72313807  -6.48775240
#>  [161] -28.79222330 -23.55683763 -27.80083068 -22.56544501 -27.59070140
#>  [166] -22.35531574 -26.59930878 -21.36392312 -21.19660089 -15.96121522
#>  [171] -20.20520827 -14.96982260 -19.99507899 -14.75969333 -19.00368637
#>  [176] -13.76830071 -18.74174898 -13.50636332 -17.75035636 -12.51497070
#>  [181] -17.54022708 -12.30484142 -16.54883446 -11.31344880 -11.14612657
#>  [186]  -5.91074091 -10.15473395  -4.91934829  -9.94460467  -4.70921901
#>  [191]  -8.95321205  -3.71782639 -14.46403835  -9.22865269 -13.47264573
#>  [196]  -8.23726006 -13.26251645  -8.02713079 -12.27112383  -7.03573817
#>  [201]  -6.86841594  -1.63303028  -5.87702332  -0.64163765  -5.66689404
#>  [206]  -0.43150838  -4.67550142   0.55988424  -4.41356403   0.82182163
#>  [211]  -3.42217141   1.81321425  -3.21204214   2.02334353  -2.22064951
#>  [216]   3.01473615   3.18205838   8.41744404   4.17345100   9.40883666
#>  [221]   4.38358027   9.61896594   5.37497290  10.61035856 -11.69411234
#>  [226]  -6.45872667 -10.70271972  -5.46733405 -10.49259044  -5.25720477
#>  [231]  -9.50119782  -4.26581215  -4.09848993   1.13689574  -3.10709731
#>  [236]   2.12828836  -2.89696803   2.33841764  -1.90557541   3.32981026
#>  [241]  -1.64363802   3.59174765  -0.65224540   4.58314027  -0.44211612
#>  [246]   4.79326955   0.54927650   5.78466217   5.95198439  11.18737006
#>  [251]   6.94337701  12.17876268   7.15350629  12.38889196   8.14489891
#>  [256]  13.38028458 -40.11586786 -34.88048219 -39.12447524 -33.88908957
#>  [261] -38.91434596 -33.67896029 -37.92295334 -32.68756767 -32.52024545
#>  [266] -27.28485978 -31.52885283 -26.29346716 -31.31872355 -26.08333788
#>  [271] -30.32733093 -25.09194526 -30.06539354 -24.83000787 -29.07400092
#>  [276] -23.83861525 -28.86387164 -23.62848597 -27.87247902 -22.63709335
#>  [281] -22.46977113 -17.23438546 -21.47837851 -16.24299284 -21.26824923
#>  [286] -16.03286356 -20.27685661 -15.04147094 -37.34594185 -32.11055618
#>  [291] -36.35454923 -31.11916356 -36.14441995 -30.90903428 -35.15302733
#>  [296] -29.91764166 -29.75031944 -24.51493377 -28.75892682 -23.52354115
#>  [301] -28.54879754 -23.31341187 -27.55740492 -22.32201925 -27.29546753
#>  [306] -22.06008186 -26.30407491 -21.06868924 -26.09394563 -20.85855996
#>  [311] -25.10255301 -19.86716734 -19.69984512 -14.46445945 -18.70845250
#>  [316] -13.47306683 -18.49832322 -13.26293755 -17.50693060 -12.27154493
#>  [321] -23.01775690 -17.78237123 -22.02636428 -16.79097861 -21.81623500
#>  [326] -16.58084933 -20.82484238 -15.58945671 -15.42213449 -10.18674882
#>  [331] -14.43074187  -9.19535620 -14.22061259  -8.98522692 -13.22921997
#>  [336]  -7.99383430 -12.96728258  -7.73189691 -11.97588996  -6.74050429
#>  [341] -11.76576068  -6.53037501 -10.77436806  -5.53898239  -5.37166017
#>  [346]  -0.13627450  -4.38026755   0.85511812  -4.17013827   1.06524740
#>  [351]  -3.17874565   2.05664002 -20.24783088 -15.01244522 -19.25643826
#>  [356] -14.02105260 -19.04630899 -13.81092332 -18.05491636 -12.81953070
#>  [361] -12.65220847  -7.41682281 -11.66081585  -6.42543019 -11.45068658
#>  [366]  -6.21530091 -10.45929395  -5.22390829 -10.19735656  -4.96197090
#>  [371]  -9.20596394  -3.97057828  -8.99583467  -3.76044900  -8.00444205
#>  [376]  -2.76905638  -2.60173415   2.63365151  -1.61034153   3.62504413
#>  [381]  -1.40021226   3.83517341  -0.40881964   4.82656603 -20.91368433
#>  [386] -15.67829866 -19.92229171 -14.68690604 -19.71216243 -14.47677676
#>  [391] -18.72076981 -13.48538414 -13.31806192  -8.08267625 -12.32666930
#>  [396]  -7.09128363 -12.11654002  -6.88115435 -11.12514740  -5.88976173
#>  [401] -10.86321001  -5.62782434  -9.87181739  -4.63643172  -9.66168811
#>  [406]  -4.42630244  -8.67029549  -3.43490982  -3.26758760   1.96779807
#>  [411]  -2.27619498   2.95919069  -2.06606570   3.16931997  -1.07467308
#>  [416]   4.16071259 -18.14375832 -12.90837265 -17.15236570 -11.91698003
#>  [421] -16.94223642 -11.70685075 -15.95084380 -10.71545813 -10.54813591
#>  [426]  -5.31275024  -9.55674329  -4.32135762  -9.34661401  -4.11122834
#>  [431]  -8.35522139  -3.11983572  -8.09328400  -2.85789833  -7.10189138
#>  [436]  -1.86650571  -6.89176210  -1.65637643  -5.90036948  -0.66498381
#>  [441]  -0.49766159   4.73772408   0.49373103   5.72911670   0.70386031
#>  [446]   5.93924598   1.69525293   6.93063860  -3.81557337   1.41981230
#>  [451]  -2.82418075   2.41120492  -2.61405147   2.62133420  -1.62265885
#>  [456]   3.61272682   3.78004904   9.01543471   4.77144166  10.00682733
#>  [461]   4.98157094  10.21695661   5.97296356  11.20834923   6.23490095
#>  [466]  11.47028662   7.22629357  12.46167924   7.43642285  12.67180852
#>  [471]   8.42781547  13.66320114  13.83052336  19.06590903  14.82191598
#>  [476]  20.05730165  15.03204526  20.26743093  16.02343788  21.25882355
#>  [481]  -1.04564735   4.18973832  -0.05425473   5.18113094   0.15587455
#>  [486]   5.39126021   1.14726717   6.38265283   6.54997506  11.78536073
#>  [491]   7.54136768  12.77675335   7.75149696  12.98688262   8.74288958
#>  [496]  13.97827524   9.00482697  14.24021263   9.99621959  15.23160525
#>  [501]  10.20634887  15.44173453  11.19774149  16.43312715  16.60044938
#>  [506]  21.83583504  17.59184200  22.82722767  17.80197128  23.03735694
#>  [511]  18.79336390  24.02874956 -24.02874956 -18.79336390 -23.03735694
#>  [516] -17.80197128 -22.82722767 -17.59184200 -21.83583504 -16.60044938
#>  [521] -16.43312715 -11.19774149 -15.44173453 -10.20634887 -15.23160525
#>  [526]  -9.99621959 -14.24021263  -9.00482697 -13.97827524  -8.74288958
#>  [531] -12.98688262  -7.75149696 -12.77675335  -7.54136768 -11.78536073
#>  [536]  -6.54997506  -6.38265283  -1.14726717  -5.39126021  -0.15587455
#>  [541]  -5.18113094   0.05425473  -4.18973832   1.04564735 -21.25882355
#>  [546] -16.02343788 -20.26743093 -15.03204526 -20.05730165 -14.82191598
#>  [551] -19.06590903 -13.83052336 -13.66320114  -8.42781547 -12.67180852
#>  [556]  -7.43642285 -12.46167924  -7.22629357 -11.47028662  -6.23490095
#>  [561] -11.20834923  -5.97296356 -10.21695661  -4.98157094 -10.00682733
#>  [566]  -4.77144166  -9.01543471  -3.78004904  -3.61272682   1.62265885
#>  [571]  -2.62133420   2.61405147  -2.41120492   2.82418075  -1.41981230
#>  [576]   3.81557337  -6.93063860  -1.69525293  -5.93924598  -0.70386031
#>  [581]  -5.72911670  -0.49373103  -4.73772408   0.49766159   0.66498381
#>  [586]   5.90036948   1.65637643   6.89176210   1.86650571   7.10189138
#>  [591]   2.85789833   8.09328400   3.11983572   8.35522139   4.11122834
#>  [596]   9.34661401   4.32135762   9.55674329   5.31275024  10.54813591
#>  [601]  10.71545813  15.95084380  11.70685075  16.94223642  11.91698003
#>  [606]  17.15236570  12.90837265  18.14375832  -4.16071259   1.07467308
#>  [611]  -3.16931997   2.06606570  -2.95919069   2.27619498  -1.96779807
#>  [616]   3.26758760   3.43490982   8.67029549   4.42630244   9.66168811
#>  [621]   4.63643172   9.87181739   5.62782434  10.86321001   5.88976173
#>  [626]  11.12514740   6.88115435  12.11654002   7.09128363  12.32666930
#>  [631]   8.08267625  13.31806192  13.48538414  18.72076981  14.47677676
#>  [636]  19.71216243  14.68690604  19.92229171  15.67829866  20.91368433
#>  [641]  -4.82656603   0.40881964  -3.83517341   1.40021226  -3.62504413
#>  [646]   1.61034153  -2.63365151   2.60173415   2.76905638   8.00444205
#>  [651]   3.76044900   8.99583467   3.97057828   9.20596394   4.96197090
#>  [656]  10.19735656   5.22390829  10.45929395   6.21530091  11.45068658
#>  [661]   6.42543019  11.66081585   7.41682281  12.65220847  12.81953070
#>  [666]  18.05491636  13.81092332  19.04630899  14.02105260  19.25643826
#>  [671]  15.01244522  20.24783088  -2.05664002   3.17874565  -1.06524740
#>  [676]   4.17013827  -0.85511812   4.38026755   0.13627450   5.37166017
#>  [681]   5.53898239  10.77436806   6.53037501  11.76576068   6.74050429
#>  [686]  11.97588996   7.73189691  12.96728258   7.99383430  13.22921997
#>  [691]   8.98522692  14.22061259   9.19535620  14.43074187  10.18674882
#>  [696]  15.42213449  15.58945671  20.82484238  16.58084933  21.81623500
#>  [701]  16.79097861  22.02636428  17.78237123  23.01775690  12.27154493
#>  [706]  17.50693060  13.26293755  18.49832322  13.47306683  18.70845250
#>  [711]  14.46445945  19.69984512  19.86716734  25.10255301  20.85855996
#>  [716]  26.09394563  21.06868924  26.30407491  22.06008186  27.29546753
#>  [721]  22.32201925  27.55740492  23.31341187  28.54879754  23.52354115
#>  [726]  28.75892682  24.51493377  29.75031944  29.91764166  35.15302733
#>  [731]  30.90903428  36.14441995  31.11916356  36.35454923  32.11055618
#>  [736]  37.34594185  15.04147094  20.27685661  16.03286356  21.26824923
#>  [741]  16.24299284  21.47837851  17.23438546  22.46977113  22.63709335
#>  [746]  27.87247902  23.62848597  28.86387164  23.83861525  29.07400092
#>  [751]  24.83000787  30.06539354  25.09194526  30.32733093  26.08333788
#>  [756]  31.31872355  26.29346716  31.52885283  27.28485978  32.52024545
#>  [761]  32.68756767  37.92295334  33.67896029  38.91434596  33.88908957
#>  [766]  39.12447524  34.88048219  40.11586786 -13.38028458  -8.14489891
#>  [771] -12.38889196  -7.15350629 -12.17876268  -6.94337701 -11.18737006
#>  [776]  -5.95198439  -5.78466217  -0.54927650  -4.79326955   0.44211612
#>  [781]  -4.58314027   0.65224540  -3.59174765   1.64363802  -3.32981026
#>  [786]   1.90557541  -2.33841764   2.89696803  -2.12828836   3.10709731
#>  [791]  -1.13689574   4.09848993   4.26581215   9.50119782   5.25720477
#>  [796]  10.49259044   5.46733405  10.70271972   6.45872667  11.69411234
#>  [801] -10.61035856  -5.37497290  -9.61896594  -4.38358027  -9.40883666
#>  [806]  -4.17345100  -8.41744404  -3.18205838  -3.01473615   2.22064951
#>  [811]  -2.02334353   3.21204214  -1.81321425   3.42217141  -0.82182163
#>  [816]   4.41356403  -0.55988424   4.67550142   0.43150838   5.66689404
#>  [821]   0.64163765   5.87702332   1.63303028   6.86841594   7.03573817
#>  [826]  12.27112383   8.02713079  13.26251645   8.23726006  13.47264573
#>  [831]   9.22865269  14.46403835   3.71782639   8.95321205   4.70921901
#>  [836]   9.94460467   4.91934829  10.15473395   5.91074091  11.14612657
#>  [841]  11.31344880  16.54883446  12.30484142  17.54022708  12.51497070
#>  [846]  17.75035636  13.50636332  18.74174898  13.76830071  19.00368637
#>  [851]  14.75969333  19.99507899  14.96982260  20.20520827  15.96121522
#>  [856]  21.19660089  21.36392312  26.59930878  22.35531574  27.59070140
#>  [861]  22.56544501  27.80083068  23.55683763  28.79222330   6.48775240
#>  [866]  11.72313807   7.47914502  12.71453069   7.68927430  12.92465997
#>  [871]   8.68066692  13.91605259  14.08337481  19.31876048  15.07476743
#>  [876]  20.31015310  15.28489671  20.52028238  16.27628933  21.51167500
#>  [881]  16.53822672  21.77361239  17.52961934  22.76500501  17.73974862
#>  [886]  22.97513429  18.73114124  23.96652691  24.13384913  29.36923480
#>  [891]  25.12524175  30.36062742  25.33537103  30.57075670  26.32676365
#>  [896]  31.56214932   5.82189895  11.05728462   6.81329157  12.04867724
#>  [901]   7.02342085  12.25880652   8.01481347  13.25019914  13.41752136
#>  [906]  18.65290703  14.40891398  19.64429965  14.61904326  19.85442893
#>  [911]  15.61043588  20.84582155  15.87237327  21.10775894  16.86376589
#>  [916]  22.09915156  17.07389517  22.30928084  18.06528779  23.30067346
#>  [921]  23.46799568  28.70338135  24.45938830  29.69477397  24.66951758
#>  [926]  29.90490325  25.66091020  30.89629587   8.59182497  13.82721064
#>  [931]   9.58321759  14.81860326   9.79334687  15.02873253  10.78473949
#>  [936]  16.02012516  16.18744738  21.42283305  17.17884000  22.41422567
#>  [941]  17.38896928  22.62435494  18.38036190  23.61574757  18.64229929
#>  [946]  23.87768495  19.63369191  24.86907758  19.84382119  25.07920685
#>  [951]  20.83521381  26.07059947  26.23792170  31.47330737  27.22931432
#>  [956]  32.46469999  27.43944360  32.67482926  28.43083622  33.66622188
#>  [961]  22.92000992  28.15539559  23.91140254  29.14678821  24.12153182
#>  [966]  29.35691748  25.11292444  30.34831010  30.51563233  35.75101800
#>  [971]  31.50702495  36.74241062  31.71715423  36.95253989  32.70854685
#>  [976]  37.94393251  32.97048424  38.20586990  33.96187686  39.19726253
#>  [981]  34.17200614  39.40739180  35.16339876  40.39878442  40.56610665
#>  [986]  45.80149231  41.55749927  46.79288494  41.76762855  47.00301421
#>  [991]  42.75902117  47.99440683  25.68993593  30.92532160  26.68132855
#>  [996]  31.91671422  26.89145783  32.12684350  27.88285045  33.11823612
#> [1001]  33.28555834  38.52094401  34.27695096  39.51233663  34.48708024
#> [1006]  39.72246591  35.47847286  40.71385853  35.74041025  40.97579592
#> [1011]  36.73180287  41.96718854  36.94193215  42.17731782  37.93332477
#> [1016]  43.16871044  43.33603266  48.57141833  44.32742528  49.56281095
#> [1021]  44.53755456  49.77294023  45.52894718  50.76433285
#> 
#> $exact
#> [1] TRUE
#> 
#> attr(,"class")
#> [1] "permutationTest"

  #Results of Hypothesis Test
  #--------------------------
  #
  #Null Hypothesis:                 Mean (Median) = 5
  #
  #Alternative Hypothesis:          True Mean (Median) is greater than 5
  #
  #Test Name:                       One-Sample Permutation Test
  #                                 (Exact)
  #
  #Estimated Parameter(s):          Mean = 9.977294
  #
  #Data:                            dat
  #
  #Sample Size:                     10
  #
  #Test Statistic:                  Sum(x - 5) = 49.77294
  #
  #P-value:                         0.001953125


  # Plot the results of the test 
  #-----------------------------
  dev.new()
  plot(test.list)

  #==========

  # The guidance document "Supplemental Guidance to RAGS: Calculating the 
  # Concentration Term" (USEPA, 1992d) contains an example of 15 observations 
  # of chromium concentrations (mg/kg) which are assumed to come from a 
  # lognormal distribution.  These data are stored in the vector 
  # EPA.92d.chromium.vec.  Here, we will use the permutation test to test 
  # the null hypothesis that the mean (median) of the log-transformed chromium 
  # concentrations is less than or equal to log(100 mg/kg) vs. the alternative 
  # that it is greater than log(100 mg/kg).  Note that we *cannot* use the 
  # permutation test to test a hypothesis about the mean on the original scale 
  # because the data are not assumed to be symmetric about some mean, they are 
  # assumed to come from a lognormal distribution.
  #
  # We will sample from the permutation distribution.
  # (Note: setting the argument seed=542 allows you to reproduce this example).

  test.list <- oneSamplePermutationTest(log(EPA.92d.chromium.vec), 
    mu = log(100), alternative = "greater", seed = 542) 

  test.list
#> $statistic
#> Sum(x - 4.60517) 
#>        -3.398017 
#> 
#> $parameters
#> NULL
#> 
#> $p.value
#> [1] 0.751
#> 
#> $estimate
#>     Mean 
#> 4.378636 
#> 
#> $null.value
#> Mean (Median) 
#>       4.60517 
#> 
#> $alternative
#> [1] "greater"
#> 
#> $method
#> [1] "One-Sample Permutation Test\n                                 (Based on Sampling\n                                 Permutation Distribution\n                                 5000 Times)"
#> 
#> $estimation.method
#> NULL
#> 
#> $sample.size
#>  n 
#> 15 
#> 
#> $data.name
#> [1] "log(EPA.92d.chromium.vec)"
#> 
#> $bad.obs
#> [1] 0
#> 
#> $stat.dist
#>    [1]   9.116805518   4.935995078   5.816558414  -6.549141922   0.802882019
#>    [6]   3.976048757   3.950410603  -3.412584350  -2.924464331  -5.777001049
#>   [11]   3.645358635   8.672958781  -5.460918719  -4.563570994  -1.842487264
#>   [16]  -4.541408080  -2.962373592  -7.116419913  -3.403709152   7.522598066
#>   [21]  -7.057934111  -5.619968019   1.316421390   0.519515467  -6.698631455
#>   [26]   3.975823905   3.037735726  -1.792458511   5.684278809   8.480103874
#>   [31]  -7.490505572   4.648768379  -0.265572543  -4.117059040  -4.159150311
#>   [36]  -3.716463934   1.082405904  -4.279865100   1.504197085   2.312770402
#>   [41]   2.447049008   0.018184890   2.819450216  -3.865827981  -1.234624571
#>   [46]   6.846847399   1.448057467  -2.415993806  -2.255646227  -7.641607632
#>   [51]   5.908348055  -2.925820723  -6.524099876  -8.247893195  -3.863690087
#>   [56]   6.255038090   1.630975012  -1.603216353  -0.204997241   3.607870903
#>   [61]  -0.514804601   7.683841479   2.220391637  -5.243361925  -0.463299609
#>   [66]  -1.623592206   6.672315820  -3.880559025   1.148812508   2.029771278
#>   [71]  -3.904379851  -4.774067174  -0.399207621  -4.471841851  -5.563362334
#>   [76]  -1.266190501  -7.521299786   9.011965654   6.146615626   7.853890873
#>   [81]   2.635268370  -2.827187010   0.647893554  -3.118711027   0.284155213
#>   [86]   0.651221101   1.834313237  -2.135113529  -3.901082571  -1.397555634
#>   [91]   0.708504253  -7.385665708 -10.756054758  -1.175167209  -3.078671293
#>   [96]  10.854435246   1.256356816  -3.549895829  -1.168012148  -8.720455077
#>  [101]   7.346558573   1.164312057  -3.193654484  -0.489885295   2.777263788
#>  [106]   4.753364737   8.551772780  -1.500389076   0.967732354  -4.460331028
#>  [111]  -1.122720818  -4.169869175   6.583832419   0.304083570   4.818296339
#>  [116]   7.610203311   4.348667953   4.705334984   5.775702769   3.834423661
#>  [121]  -2.507441719   0.561474280  -5.829332658  -4.618701403  -2.509199188
#>  [126]   5.077230212  -2.976954458   1.528497894   2.415993806   0.268226296
#>  [131]   5.855901664   4.953655237   4.681879839  -3.692303347  -1.115948298
#>  [136]   4.937332423  -3.152478093 -10.198368510  -3.105412615   0.098809325
#>  [141]  -8.672080626  -8.019879433   1.583484175   1.190998935  -2.216659858
#>  [146]  -0.309368747  -3.689006066  -1.326864442  -2.099727468   2.889980718
#>  [151]   2.275522047  11.154312108  -5.665281305   2.516730017  -0.788337468
#>  [156]   0.661683200  -1.030462820   7.385665708   7.185854272   4.093001210
#>  [161]   0.814486351   7.388962988  -3.727689408 -11.138375768   7.641607632
#>  [166]  -7.197044349  -0.109471193  -2.516730017   9.788118418  -2.650365095
#>  [171]   0.602409847  -1.423853142  -1.993540969  -3.147646461  -5.097158569
#>  [176]   7.516883149  -1.490566495  -1.459890153  -0.680505655  -7.259856184
#>  [181]   4.887782236  -6.469515591   5.102976284   0.418625249  -4.093426750
#>  [186]  -0.773825818   1.949767641   2.812711675  -8.270065886   5.934172522
#>  [191]   4.241410451  -1.180786392  -4.730691094  -4.921311453  -0.666099838
#>  [196]   1.161368764  -3.654522454  -1.659813225   1.399825579  -5.649795196
#>  [201]   0.315923279   2.708430668   8.102199501  -7.069235825   5.871360687
#>  [206]   9.557101603  -2.002833924  -2.824084842   7.329342081  -1.322411488
#>  [211]   5.031089389   4.857553651   5.212416794   2.841549888 -11.160108013
#>  [216]   6.475140009   2.384971846  -2.902952546   1.799657309   5.775702769
#>  [221]   2.610456833   4.199006036  -2.365252189   6.814285628   2.598980869
#>  [226]  -0.076525645   1.943971736  -3.890626521   2.232571506  -8.926390977
#>  [231]  -4.508084680  -0.299264936   3.710462211   3.003034125  -0.510445156
#>  [236]   1.303960290  -9.731980736   0.506543639  -3.143923641  -4.422272618
#>  [241]   8.883954994   3.983005286  -5.896010614  -7.195045348  -0.241289862
#>  [246]  -6.736005811  -4.914354925  -0.326385378  -5.371820081   1.446883666
#>  [251]  -0.680689663  -2.028925614   6.292912492  -5.151622087  -5.117339162
#>  [256]  -6.866233460   0.317112932   0.972393417  -8.399904978  -2.989510714
#>  [261]  -4.426029088  -5.009996990   2.763326450   8.921554215  -4.426213096
#>  [266]  -3.557829629   5.477722110  -0.666270406   0.445123592   2.999063090
#>  [271]  -2.230008072  -9.744183481  -1.603837152  10.192653592   1.795755791
#>  [276]   1.442229994 -10.145501996   4.110466256   2.961857734   2.373955072
#>  [281]   6.731589174  -1.801551697   0.516803602   0.239035251   6.326924065
#>  [286]  -4.626893558   6.470505383   5.312957893  -1.547253867   8.460686246
#>  [291]  -3.266576106  11.542429024  -5.271440592   0.517167347  -0.095453933
#>  [296] -13.133924611   3.546598548  -2.827187010   1.492686262  -1.148594520
#>  [301]   8.299696058   2.550606418   4.139732683   4.392705688  -2.026485101
#>  [306]   8.399904978  -1.197025350  -7.615240761  -0.508813583  -0.645710545
#>  [311]   0.577410619  -0.266964332   0.328384379  -6.907628667  -3.267656397
#>  [316]   0.415545957  -1.920137470   1.837427098   1.863322609  -4.068909440
#>  [321]  -7.679206853  -4.978228924   0.925234430   0.428102213   5.433265739
#>  [326]   1.874405507   7.250900655   3.811059688   3.420482276  -6.866233460
#>  [331]  -0.468792896  -7.167477419  -1.716948684  -0.385604289  -7.495150904
#>  [336]  12.405993857  -2.750744584  -2.275000613  -2.639902996 -10.587372461
#>  [341]  -1.962323897  -5.550793909  -3.058100328  -2.093074795  -5.149623086
#>  [346]  -5.271658580   7.067097930  -2.685250704  -0.028314220   0.259137858
#>  [351]  -4.893785775   1.793630895  -0.462001329   2.568052418  -4.486605807
#>  [356]   4.978228924   4.574429040  -1.984251254   3.270371944  -1.311306781
#>  [361]   0.096246719 -11.961268964   7.536960945  -2.430538357  -7.015529696
#>  [366]  -5.264583442   7.127879198   4.675704813  -4.402355954   0.376533978
#>  [371]   1.372763144  -0.252383465  -8.923473294  -1.175167209  -1.946676179
#>  [376]  -0.658567592  -1.732416666   5.155133642  -1.790919030  -5.626156043
#>  [381]   1.038816584   0.333019005   0.270409305   9.391480471   2.203916383
#>  [386]   3.289410452   1.426565007  -0.916164120   1.438962864   3.032170248
#>  [391]   2.697235461  -1.482920677   3.995924577   0.919519512  -6.042983542
#>  [396]  -0.283328596   3.223721459   3.401935003  -1.642796594  -1.239456203
#>  [401]  -6.282966251  -3.606492701  -0.431544541   1.446665678   6.373989543
#>  [406]   3.040908527  -1.075408532  -1.381619295   3.831344368   4.848840063
#>  [411]  -9.418927633   1.604055140  -3.995987819  -5.723144742   1.868050744
#>  [416]  -5.165367995  -3.802288167  -5.070607689  -4.581327047   0.479406517
#>  [421]  -8.873524462  -0.588490635  -3.470085490   1.379724907  -7.116419913
#>  [426]  10.050062066  -3.779073634  -2.268228092   8.603277772   0.575858967
#>  [431]  -3.466788209  -8.630724935   1.570070085   3.977547725   4.894599871
#>  [436]  -3.442156409  -9.054199501   3.823423566  -0.618057565  -6.452065289
#>  [441]   0.315923279  -4.935995078  -5.601958741   3.265737318   2.421835474
#>  [446]   0.133328335   3.941340292  -3.334142923  -0.243288862   0.369979446
#>  [451]  -1.638677826   4.953211569  -3.605871902  -4.489903087   4.689687266
#>  [456]   2.945138973   4.125763669  -1.019432458  11.770648605  -4.666933292
#>  [461]  -0.535180454  -1.371551799  -9.976819699  -4.725274046  -8.292819860
#>  [466]  -3.650275318   2.258846285  -4.236582528  -3.287836991   5.491957359
#>  [471]  -0.066247554   7.730716975 -11.133741143  -4.700336613  -4.406624899
#>  [476]  -1.523419601  -2.184759742  -1.692740677   6.582074949  -3.085547490
#>  [481]   6.047400180   5.796169121  -0.580126166   0.651221101   4.141030962
#>  [486]  -3.491830255  -9.934585852   6.366154859   5.382282180   5.005160229
#>  [491]   0.517167347  -0.418625249   2.262418747   2.961293300  -3.681016048
#>  [496]  -7.487230101   3.250455758  -3.674277507   6.204590700   1.322229816
#>  [501]   1.255000423  -6.022664882  -8.443861045   6.253681698  -1.751820854
#>  [506]  -0.619815034  -2.945138973   6.778410227   3.314329758  -1.584821520
#>  [511]   6.697551163   0.725543760  -2.569590482   3.101851257  -5.270103247
#>  [516]  -0.746298734  -7.684944646   7.634261141   9.896028407   5.290858221
#>  [521]  -5.666159461   1.426782995  -3.227990405  -5.444891880   2.688134884
#>  [526]  -2.519441882  -7.396770415  -6.448955730  -2.095092842  -0.372691311
#>  [531]   5.541688202   9.281059007  -2.405531707  -2.682849707   5.541688202
#>  [536]   3.081750585   9.163260890   2.390063726   0.764480326   0.601072501
#>  [541]  -8.997996640 -11.196350842   1.361152942   9.356535922  -1.036897505
#>  [546]  -0.696166813  -1.839131871   7.771193500  -3.732400274  -0.173332672
#>  [551]  -2.898683601  -4.145351866   8.288185234  -6.055226653   4.629013325
#>  [556]  -0.516821729   3.045543153   4.629013325  -0.961730630  -6.384899138
#>  [561]  -7.780447818  -4.747568831   0.629346281   1.905299100   0.678852272
#>  [566]  -4.711336708  -2.067145634   0.087533130   0.344560094   5.601958741
#>  [571]   3.478457350  -4.389626396   0.323306086   1.974784996  -1.715189468
#>  [576]  -9.333505397  -4.607877926  -1.494580650  -1.698742401   5.477538102
#>  [581]   0.137125240  -5.034364861   2.792313093   2.074697943  -2.067880308
#>  [586]   2.011904235   0.794110498   0.894489987   6.071253493  -0.658567592
#>  [591]   4.257692409   3.425682074  -2.507807400  -0.106166522  -4.357257802
#>  [596]   0.744541264   5.224985220   2.403091194  -4.912137936  -3.609208248
#>  [601] -10.522108089   0.977028043   3.088938279  -1.075570141   0.273736852
#>  [606]  -2.600979870   5.915156891  -4.729542991   3.563435919  -3.750154761
#>  [611]   0.141541877   4.152332676  -5.014631616   2.177987222  -1.350825081
#>  [616]   9.192155482  -0.002707740   4.791083805  -0.779110995  -1.559651724
#>  [621]   9.541360376   6.322289439   1.716016085  -2.124865589   2.070442915
#>  [626]  -4.448312768   5.781119816  -0.682424734   3.282758698   7.271367008
#>  [631]   5.669915931  -6.587422440   3.889799904   0.884071626  -2.540144319
#>  [636]   6.364317468  -8.480103874  -8.815549389   7.141896458   3.732802270
#>  [641]  -4.846570119  -1.731700119   3.378295849   0.063698864  -0.211884542
#>  [646]   4.886609852  -1.175949630  10.150614858  -5.939945552  -2.770454952
#>  [651]  -6.319848926  -8.480103874   4.357257802  -1.237336436   5.104757296
#>  [656]   3.372815560   9.891191645  -9.531888988   1.249191997  -8.617094344
#>  [661]  -3.534799104  -2.809780075  -5.805550928  -7.939313109  -6.147587291
#>  [666]   4.808350099  -3.454818197   0.215761778  -0.452470083   7.986545328
#>  [671]  -0.576247524   2.618794035   4.759173163   2.010378340  -0.923936150
#>  [676]  -7.388745000  -0.593264155  -3.137897227  -8.423762120  -6.656033863
#>  [681]  -0.500885390   2.038089433  -1.411515702   4.062256767   2.843105222
#>  [686]   0.622894326   1.003964477  -1.528693006  -2.403011273   2.293547886
#>  [691]   1.228598156  -7.424620402  -4.495698993 -10.714026729  -5.457621438
#>  [696]  -0.936518016  -6.484831131  -6.275413943  -1.614820685   0.479235948
#>  [701]   3.313962330   1.924738116   1.613646884   1.804267244   0.465437503
#>  [706]   3.828058192  -2.097728467   3.864679879   6.401897642   5.168849284
#>  [711]   2.259064273   5.880074275  -1.547253867  -5.254271520  -7.077667356
#>  [716]   3.690304346   4.415901175   6.600250967   4.636934127   3.793574579
#>  [721]  -0.208989258 -11.530918201  -4.098626547   2.705133388  -3.850360000
#>  [726]  -0.427643023   3.546816537  -5.668158461   1.712477603   3.647357635
#>  [731]   2.814412766   2.372598680   0.429274596  -8.160861920   4.958289862
#>  [736]  -2.283714201  -3.221009595   9.164559170  -1.258446316  -9.339912237
#>  [741]  -6.257037090  -1.186582298   4.080420263  -4.956566043  -6.495043675
#>  [746]   4.765945683   3.987274231  -0.294411494   0.096246719   0.970748404
#>  [751]  -0.666488394  -5.053189062  -2.781873723  -4.232111447   0.619449353
#>  [756]  -1.529835239   4.742934205   1.144543563  -4.343831191  -6.262845517
#>  [761]   2.507441719  -0.293055102   3.563435919  -3.885146231   1.549969414
#>  [766]  -2.321455985  -1.724295175  -0.808677924  -4.524021019   5.907010709
#>  [771]  -7.833526271  -5.585082409  -4.291384801  -4.648768379   4.260610092
#>  [776]  -4.406624899  -9.011965654   9.391480471   6.193070999  -3.287836991
#>  [781]   1.463004014   1.849593970  -5.499660173   5.219637730  -0.660291412
#>  [786]   2.686240496   3.895034360  -2.852377668   1.308594916   1.014797833
#>  [791]   3.083312942  -6.057346421   4.454121195   2.600612442   3.158193011
#>  [796]  -0.202814232   1.186582298  -1.380570571  -1.234864355   3.223721459
#>  [801]   8.619214111   4.428081044   3.389128285   3.105412615  -4.478311933
#>  [806]  -5.889800781   2.699360358  -5.947682346  -2.432297573   2.845306358
#>  [811]  -0.858858092  -7.708583800  -2.984473264   4.814159444  -0.397426609
#>  [816]  -1.348906002   7.827960793  -3.900461771  -0.254503232   5.590958646
#>  [821]   1.384378579  -3.839058287  -7.260572731  -6.429844850  -0.658056864
#>  [826]  -4.207961566   7.520678987   0.204997241   3.095710800   2.800250575
#>  [831]   7.452746488  -7.642905912  -0.517883894  -1.695663108  -2.012561349
#>  [836]   2.643384285  -0.627163272  -2.728990530   1.419218516   5.037541344
#>  [841]   2.129957469  -3.282574689  -4.223010871   7.772745004  -1.857527770
#>  [846]   1.186411729   2.182403860   4.662462211   1.771921525   0.166777221
#>  [851]  -6.390672168   2.214911348   1.570364313   1.601690459   2.931790759
#>  [856]  -6.018604967   8.107995406   5.663925832  -1.748064384  -9.896028407
#>  [861]   6.489247769   3.166023314  -1.673541037  -5.841793757   2.491333064
#>  [866]  -1.175949630   4.623355076   0.492964588  -3.311694132  -1.545496397
#>  [871]  -3.330266097  -9.472557523  -5.402853145   1.072554091  -7.250900655
#>  [876]  -4.931353428  -4.423664406   5.694740908   1.759353100   3.841770151
#>  [881]  12.752683892  -0.241750798   6.055226653  11.600404098   4.581327047
#>  [886]   1.439146872   2.349403193   3.460165687   4.050596795   5.516894792
#>  [891]  -8.417292038  -1.635391650   2.011904235   6.783157408  -4.626893558
#>  [896]   0.303367024  -4.338242170   1.796727456   5.896010614   0.658567592
#>  [901]   1.689661385  12.443593078   6.642685648  -2.824084842  -2.138389000
#>  [906]  -0.925234430   5.939968428   3.442249918   9.774019470  -4.071179385
#>  [911]   0.009262272  -1.599420514   0.896488988   0.199516951  -9.024426753
#>  [916]  -1.903461709  -4.553674067   8.630214206  -1.145721046   6.720528662
#>  [921]  -1.969499819  -0.819140023   3.653166062  11.806685616  -1.377032089
#>  [926]  -0.257018091   4.113181803   2.214911348   2.173333549   3.033927717
#>  [931]   4.672625520  -7.240840553  -1.529835239  -2.008824942  -1.148996517
#>  [936]  -5.559554326  -0.786067524  -3.275657121  -6.102292132   1.350825081
#>  [941]   2.209115442   1.378369434   2.430298572   0.320192224   5.264583442
#>  [946]   3.502314492  11.642637945   3.152478093   4.159150311  -5.393507654
#>  [951]   0.700972007  -2.101779424   6.324288439   2.158782833  -4.389408408
#>  [956]   8.341051749   1.571242469 -11.811320242   1.181758057   1.295838800
#>  [961]   0.711434106   5.815586750  -7.456988996   4.803513337   3.034805873
#>  [966]  -7.390136789   5.752063615  -5.159768268  -7.385665708  -6.779802015
#>  [971]   2.651606706  -1.461647622  -1.892838000   0.485031854  -1.379743954
#>  [976]   6.339505930  -2.755576216  -7.782446819   4.511841150  -2.431930145
#>  [981]  -6.121036412   1.338072647  -1.619455311  -2.698062078  -2.050342243
#>  [986]  -8.006759571  -1.555765319  -4.889119581  -2.287983146   8.978120820
#>  [991]   5.090202040  -8.197725549  -3.821303799   7.744815923   1.151730191
#>  [996]  -0.876124386  -2.520268499  -5.775702769  -2.650549103  -1.940674455
#> [1001]  -5.927400002   0.321914297  -4.150976284  -0.794110498  -3.752696058
#> [1006]  -1.383011083   0.182897568   0.291501704   1.337513789   0.571590022
#> [1011]   4.522836115  -3.292104189   5.290858221  -2.182403860   3.838325178
#> [1016]   3.559166974   0.429655611   1.014613824   7.429255028  -5.565199726
#> [1021]   3.226598616   6.990794398  10.145501996   3.810002085  -6.512278294
#> [1026]  -2.432663254  -1.444771290  -6.720344653  -0.773825818   1.840488263
#> [1031]  -7.849187430  -3.486021829   8.548509479   3.837760007  -1.190998935
#> [1036]   2.651147517  -1.600757860  -3.288054979   0.401747512  -2.184541754
#> [1041]   4.528460533   1.505042749   1.938684743  -7.828891645   4.493258480
#> [1046]  -5.501579252   1.354714428  -1.706852266   3.225445279   1.423853142
#> [1051]   1.509459386  -2.204077992   3.853075547   2.846184514  -4.364596870
#> [1056]  -6.314586624  -3.047437541  -5.582736225  -2.811539291   0.607062600
#> [1061]   0.749654126  -4.215664380   0.235942372   0.308966751  -7.118602923
#> [1066]   0.629121429   3.559627910   3.672007563   0.479235948  -2.300017968
#> [1071]  -0.139101365   0.793048334  -3.568698221   5.638712298   2.910352741
#> [1076]   3.765327726  -3.191735405  -9.224717253  -9.557101603   3.120630106
#> [1081]   5.090202040   6.364523286  -6.866233460   2.299356313   7.119901202
#> [1086]   1.339053270  -1.928035396   0.913723607  -9.908426264   4.495698993
#> [1091]   9.059291381  -1.394219288   7.939313109 -12.001940601  -3.546414540
#> [1096]  -1.467272959  -1.834313237  -1.995539970   4.785150072  -2.760210842
#> [1101]  -4.889119581  -1.824674664   0.843380942  -4.019758843   3.927380078
#> [1106]   6.251264061  -7.605763798   9.668821347  -2.919426881   3.224088887
#> [1111]   2.196364074   7.006262380   7.887744875   0.257800513  -0.270409305
#> [1116]  -6.587789867   0.644832389  -5.329415666   1.246975008   1.565617132
#> [1121]   4.088348457  -1.876363665   0.846678223  -4.656666305  -3.038196662
#> [1126]   0.735073260   2.302458481   3.033101100   5.315306012   0.783866387
#> [1131]   4.080420263  -5.353467920  -7.476568234  -1.648511512   1.892838000
#> [1136]  -3.283401306  -1.611219959   4.655949759  10.942040491  -4.539288313
#> [1141]  -3.546414540  -0.649467015   5.351468920   3.016061593   0.658567592
#> [1146]   3.651246983   3.224088887  -1.485838360  -0.246575039  -3.601400821
#> [1151]   0.067639343   5.005676087  -5.374579366  -5.286756132   2.888050933
#> [1156]   4.626893558  -1.610931337   0.740583816   5.062661369  -7.305886936
#> [1161]  -3.610276019   3.330787531  11.660025005  -2.741226777 -10.529179399
#> [1166]   1.295659063   1.879660945   2.805730865   1.339432868   1.130435656
#> [1171]  -3.598765196   7.641975060  -1.801551697   1.114556510  -1.313065997
#> [1176]  -4.471841851   1.064380064   3.504950117   2.324385838  -2.677502217
#> [1181]  -0.576224648  -0.027140419  -2.613386686   4.522053693  -2.810712674
#> [1186]  -6.512909798  -0.241750798   6.509623622   2.898683601   1.483379867
#> [1191]  -0.287028688  -1.299946135  -2.090439170  -5.357264825  -0.493987383
#> [1196]   1.348906002  -2.247838800   4.681879839  -4.957922435  -0.243669877
#> [1201]  -7.344639494   7.684921771  -4.725435656   0.602427974  -3.193734406
#> [1206]   0.708136826  -2.068443914 -10.007748150  -3.716681922  -2.991429793
#> [1211]   6.193288987  10.151695150  -2.946196575   5.838496477   4.541287313
#> [1216]   2.126784668   8.442930193  -4.257692409  -4.115284891   6.534561975
#> [1221]  -6.642685648   0.210344731   2.174596433  -5.155040134  -1.924738116
#> [1226]   0.003088165  -8.315850385  -0.872769912  -4.508923467  -0.947568440
#> [1231]   4.537932840   2.436346783  -7.771377508  -8.532550264  -9.166742179
#> [1236]  -2.908610794   5.989548765   4.893956343 -10.604541533  -1.801840318
#> [1241]  -1.448057467   2.596710925   4.703335984   7.911579141   1.889299518
#> [1246]  -4.730691094  -0.342014969   1.462638333  10.396752101  -4.090365585
#> [1251]   1.038654974  -2.514731016   1.597282620  -2.680616078  -1.710753784
#> [1256]  -4.449393060  -4.396582924  -7.344639494   0.677790108  -7.738043403
#> [1261]   4.170087163  -1.634054304   2.974413162   2.368842209  -4.956566043
#> [1266]  -7.843057518   9.859441706  -3.353560552   3.222790607  -2.672423924
#> [1271]   1.779281456  -5.419656537  -1.736116757   2.279060528   5.863616502
#> [1276]  -1.461246545   0.764755507  -7.948784497   7.417663873  -2.262602755
#> [1281]  -7.487230101  -3.059455800  -0.287028688   8.121422017  -5.684496797
#> [1286]   5.033651996  -0.762210382  -7.253020422   4.227844249  -5.759020144
#> [1291]  -2.035579704   0.722246479   3.647139647  -1.179488112   5.626156043
#> [1296]   5.106055576   6.973777767   0.390332423   0.458664983  -0.239480854
#> [1301]   1.771921525  -3.765327726   4.538922632  -2.805512877   5.253063740
#> [1306]  -6.321186271  -6.057346421  -3.148157190   7.099800531  -6.559975277
#> [1311]   2.889980718  10.269096018   2.344670518  -1.863322609   5.489241812
#> [1316]   7.921498944  -1.070371082   8.224551912   2.049333034   4.028922662
#> [1321]   7.401206100   8.972858519  -0.942714999   7.207506448  -2.766019268
#> [1326]   6.205468856  -1.394017152  -6.618811827   1.847324026   1.315759734
#> [1331]   5.460723607   1.260991441   0.763400035   6.452128531  -6.939257839
#> [1336]   0.474569755  -1.855068211   2.784782594  -0.326183242  -6.263063505
#> [1341]  -4.149768504   2.659320624   7.476406624  -3.181317044  -9.494289767
#> [1346]   2.741226777  -2.028925614  -6.029023328   7.550527147   9.584019910
#> [1351]  -0.850033615   3.003114046   2.583319711   1.266190501   6.129228566
#> [1356]   5.519404521  -0.485031854  -6.074581040   1.488729104  -2.780374756
#> [1361]   7.112611905   3.208235351   4.150976284  -0.768030978  -3.800896379
#> [1366]  -2.156049159   8.439593847  -7.708583800  -0.344762230   1.233232782
#> [1371]   8.370618678  -0.115267099 -10.023684490 -12.252972718   2.391401071
#> [1376]  -4.014043925   0.814486351   1.501756572   1.675080518   7.358608507
#> [1381]  -0.282807162  -0.506543639  -4.810167427  -4.115284891  -1.233326291
#> [1386]   5.562269873  -9.976819699   6.719191316   1.838764444  -0.156122744
#> [1391]  -2.294537678 -10.720017747  -2.113837122   8.543851977  -7.681125932
#> [1396]  -1.131975137  -2.702715751   3.563435919   6.525491664  -0.151875608
#> [1401]  -4.342953035   0.287028688   5.947682346  -3.490613676  -6.320727082
#> [1406]  -0.224636976   3.279558639   2.037515462   1.796727456   4.888608853
#> [1411]  -4.071179385  -1.000378576   3.270371944  -0.994894167   0.930892679
#> [1416]  -3.562925191   5.301336999   5.863616502   0.437002101  -4.731662758
#> [1421]  -3.264657027  -2.097728467  -6.173902926  -8.903154634   0.362596640
#> [1426]  -0.894305978   6.150884572  -4.243111542  -3.493724643   1.540297338
#> [1431]  -3.821303799   4.656300624  -5.524689698   1.148996517   0.331020004
#> [1436]   2.029771278  -7.389952780  -1.677430384   1.367650282  -0.025141419
#> [1441]  -8.305176347   8.172531061   2.407062230  -2.908610794   0.546451901
#> [1446]  -0.850911771   7.691544293   6.239224490   1.074691985  -6.809248178
#> [1451]   2.160304187   1.171830863  -0.518941496  -0.897787267  -5.934172522
#> [1456]  -7.579365360  -3.265737318   7.723164666   0.385697797  -1.669622957
#> [1461]  -2.407280218   4.409874760   9.276222245   7.079504747  -5.005160229
#> [1466]  -0.494883667  -4.295801439   3.501652837   5.477940098  -0.768398406
#> [1471]  -0.859650050   2.685250704   1.482541080   4.152332676   5.285675841
#> [1476]   8.295474532  -8.039807789  -1.315759734  -5.396863047   3.460992304
#> [1481]  -8.200579989  -2.198107956  -4.026381366   0.129937546   2.809414395
#> [1486]  -5.207580033  -4.761311057   9.603774963   2.423191866   7.728879584
#> [1491]   0.678668264   5.023795435  -0.769191192  10.164724512  -0.936092476
#> [1496] -11.061933343  -3.943339293   6.055226653  -0.119901724  -1.923216762
#> [1501]  -0.666488394   2.097728467  -2.129957469   5.943242833   0.991137697
#> [1506]  -3.063098699   5.986618912   2.257145194  -2.097728467   4.656471193
#> [1511]  -1.797112184  -4.098626547   3.087546491   7.099800531  -1.648511512
#> [1516]  -2.570982271  -4.303802163   3.015695912  -5.334069339  -0.382159315
#> [1521]   4.486605807 -10.568972880  -4.405458122   0.619894956   1.372378416
#> [1526]  -4.447691969  -4.820931964  -0.683505025   0.038950569   1.520133424
#> [1531]   0.943290536   0.781230762   0.571590022  -5.566900816   6.219469437
#> [1536]   0.530545828  -9.071239007  -1.042705931   3.884003998   5.927400002
#> [1541]  -1.702217640   4.479649278   5.342363213  -2.055862048  -8.032851260
#> [1546]  -3.818591934   1.011898277   0.771826817   2.313648558   1.936164309
#> [1551]   0.993502378   5.296483558   1.175949630  -3.047437541  -2.448129300
#> [1556]  -4.367470345  -7.579365360  -3.339141295   0.896409066  -6.251046072
#> [1561]  -1.734335745  -8.898737996  -4.706051530  -0.471233409   2.540144319
#> [1566]  -3.168717051  -6.554937827  -1.479112669   8.312920532   3.225445279
#> [1571]   2.610456833   0.303367024   2.180404859 -10.481367635  -4.296203435
#> [1576]  -5.835323676   4.558308693   0.618263383  -1.450056467   4.623355076
#> [1581]   2.472577091  10.523406369  -6.110212935   1.904453436   1.136244082
#> [1586]   6.130783900  -0.475868035   1.064380064   8.253240685  12.066986985
#> [1591]   8.968223893   4.888608853   9.200860111   0.399425609   8.903154634
#> [1596]  -4.719080893 -10.668231524   2.664277743  -1.254965027  -2.578685085
#> [1601]  -3.479755630   0.155777126  -3.728861792   7.095165905   4.069787596
#> [1606]  -6.456902051  -1.450056467  -7.690206948  -1.314422389   4.549234553
#> [1611]  -0.183059178  -0.623865991  -2.027658901  -5.638712298   3.191953394
#> [1616]  -1.110139872  -1.565435460 -11.084745879   6.744937388  -1.295475054
#> [1621]   9.287050025  10.667353368   6.804613552   7.070573170  -3.020348666
#> [1626]   5.418684872  -6.258428879  -3.286113171   3.507661982  -0.621814035
#> [1631]   5.521334306  -1.569191930  -1.788983271   2.973657178   1.954805091
#> [1636]   4.680523447   3.692303347  -5.033272399  -4.544580881   4.818296339
#> [1641]   5.400338287  -1.450056467   6.110212935   5.830689050  -6.093899290
#> [1646] -11.394042511   0.456331797   2.969778536   7.545892521   3.754258415
#> [1651]   2.493332065   2.131294815  -0.416442240  -7.635559421  -3.308614840
#> [1656]  -2.045707617   2.363492973   4.213769992  -0.572779675   7.011260751
#> [1661]   5.243809421  -4.278986944   3.879167237   3.399936002   4.286976962
#> [1666]   6.929556024  -3.471259290  -0.464357212   1.033542112  -0.346743104
#> [1671]   6.809432187  -0.724463468  -2.533371799   2.567080753   8.439230101
#> [1676]   0.856720198  -8.125230025   4.390706687   0.155151079  -7.700662997
#> [1681]  -1.896280328  -9.484077224   3.154748038  -1.567800141   4.650951388
#> [1686]  -0.546451901  -1.790040874   2.717990435   3.180131074  -5.415239899
#> [1691]  -2.280784348  -3.792384926  -0.501506189   4.507004388   1.332799241
#> [1696]   5.283901692   5.220718022  -5.296483558   0.075353261  -0.456192903
#> [1701]   4.104284796  -3.124168588  -2.143467293  -0.998677485  -4.346014200
#> [1706]   6.174523725   1.671621958   3.874933688   1.377179781   3.088844771
#> [1711]   3.748449988   2.651606706  -0.898757185  -3.132873217   3.434235607
#> [1716]   3.958218030  -0.582020554  -3.323493577  -8.168095377   3.378295849
#> [1721]   0.680505655   3.944419585   6.889045997   4.146323530  -4.298202436
#> [1726]  -1.855087257   1.889299518   3.070681274  -4.173625645  -0.517005738
#> [1731]   1.776431672   6.308547213  -6.104211211   6.054236862  -2.699360358
#> [1736]   2.697430574  -0.213126153   3.648531436   6.809248178   1.759353100
#> [1741]  -2.097510479   7.875347018   1.100587496   6.342860404   2.818369924
#> [1746]   3.330787531  -1.266190501  -4.475965749  -7.625671293   7.116419913
#> [1751]   3.179925256   3.224088887  11.520972880   2.725727229  11.045055606
#> [1756]  -2.367964054  -9.914427987  -7.085474783   4.113365812  -3.369007551
#> [1761]  -2.384971846  -1.793836712   6.092345892   2.809414395   1.692740677
#> [1766]   3.146819844  -0.497588109  -7.769985719   2.474701988  -5.031089389
#> [1771]   4.931353428  -6.264143797  -5.420954816  -0.827260594   3.668652170
#> [1776]  -2.243014559  -0.959811551   3.233618387   1.748891001   2.775872000
#> [1781]   4.475965749  -1.519622696  -6.009649437  -4.666933292  -1.820387592
#> [1786]   0.771110271   2.701870087   4.994165264  -1.599420514   4.343320463
#> [1791] -10.355344871  -7.286664420   0.682149553   5.668560458   7.117246531
#> [1796]   1.744245669   4.273007949 -10.108748439  -3.358195178  -4.071327077
#> [1801]  -5.031089389   5.874439979   0.663829894   3.074036667   3.415219975
#> [1806]  -5.550793909   6.744937388  -1.152350990  -6.882691233  -1.876525274
#> [1811]   7.112611905   3.491830255   1.972785996  -4.463410320  -2.479533620
#> [1816]  -2.630264423   5.325194141  -0.706780434  -6.019126400  -3.582635559
#> [1821]   1.771921525  -4.135039944  -9.274102478  -0.321949694   2.666196822
#> [1826]   6.617731535  -4.132599432   8.672242235   1.276823168  -1.924738116
#> [1831]   6.400925977  -6.864234459   1.904178255   0.754810186   5.092339934
#> [1836]   3.062018407   0.406382138  -4.203824670   1.986010470  11.154312108
#> [1841]   2.367964054  -4.291568810  -7.582756149   1.260773453  -4.592517124
#> [1846]   4.316384029   7.875347018   2.817128313  -4.491706976   0.972931413
#> [1851]   5.578101599   2.461927744  -6.645764941   4.804905125  -0.700790335
#> [1856]   6.066416731  -0.607246608   1.361152942   4.945065388  -1.706119158
#> [1861] -11.045055606 -10.079692237   6.787574046   5.387699228   0.872206306
#> [1866]  -2.449684633  -5.737145323  -0.018184890   0.813149005   0.896409066
#> [1871]  -3.940600870   4.245827089  -6.442964712   1.651902301   4.074717867
#> [1876]  -7.519962441  -3.938899780  -4.859489410   6.557855510   0.703869627
#> [1881]   2.183702140  -7.990823232   1.320838027   1.702435629  -5.444891880
#> [1886]   2.899051028   5.997251580   0.888706252  -5.503578253   6.024413393
#> [1891]   7.681125932  -2.766038315   8.804176222  -7.667188593   4.146323530
#> [1896]   8.528133626  -6.990794398   1.640676827  -1.264070734  -3.367833750
#> [1901]  -5.575022307  -4.203422674  -0.725543760   1.589292601  -3.360635690
#> [1906]  -1.456828988  -1.986521199  -6.762574818   0.529403595  10.871312983
#> [1911]  -6.804613552   1.398853914   8.078365235   3.870462607  -3.611102636
#> [1916] -10.726206598   7.992942999  -3.313962330  -5.998034001  -5.005160229
#> [1921]   3.341856842   3.285273556   3.020348666   1.821940990  -2.809320886
#> [1926]   2.275000613   3.889799904  -7.612918858  -0.230445403   0.198527159
#> [1931]  -0.583205458  -4.511841150  -5.750174685  -7.185854272  -3.003034125
#> [1936]  -6.383691358   8.173868407   8.357671131  -1.657675331   1.042705931
#> [1941]   3.873635408  -0.886957741  -2.006189317   8.453392292   0.076343972
#> [1946]   1.757228203   2.614917208   7.580573140   6.269618037   0.657414255
#> [1951]   6.458901051  -5.705390255   0.013531217  -4.520716348  -5.144275596
#> [1956]   1.254965027   6.459411780   0.896488988  -2.381188528  -0.913723607
#> [1961]   6.276712222   9.163478879 -10.180192493  -1.660605184  -4.824104765
#> [1966]  -3.719761215   2.040594755  -4.859489410  -6.088090863  -6.592537048
#> [1971]   8.169451769   2.334087653  -7.098249026  -0.883289204  -0.932082331
#> [1976]   2.215106460   7.742896844  -7.214800402   2.404389474   4.406643027
#> [1981]   6.577956182   1.058755646   5.839588939  -0.351395857  -0.833903979
#> [1986]  -5.208878312   4.702255692   3.356001065   1.354530420  -2.407280218
#> [1991]  -6.175534499   1.897819809   2.619527143  -0.927447706  -5.217431845
#> [1996]  -6.391074165  -7.012450404  -2.708524177   0.874205307   2.067145634
#> [2001]   5.661742823   0.003088165   2.065146633  -6.469113595  -6.809248178
#> [2006]  -4.260610092   0.657414255   5.006917698  -3.669077710  -6.135005425
#> [2011]  -0.678731506  -1.857527770  -4.590793305  -1.467443528  -2.733843971
#> [2016]   5.750174685   0.363977723  -2.650549103  -1.473827491  -2.766405742
#> [2021]   5.357264825   7.536960945   1.217397373   2.386672937   5.072606690
#> [2026]   3.151236482   0.257582525   0.377706362   2.888050933  -0.428481810
#> [2031]  -8.592444417   1.083762296  -9.658543256   3.765448492   7.238634668
#> [2036]  -3.096772964   4.253774329   1.807360123   5.330713946  -0.678731506
#> [2041]  -6.406551315  -8.650142563  -0.061763106   3.675978598   6.380459625
#> [2046]   2.157404632   5.806631220   6.442964712  -3.721098560   7.990823232
#> [2051]   4.173976511  -2.775872000   2.156049159   5.817856694   3.735818321
#> [2056]  -5.406053204   1.565653448   3.495844410  -0.726881105   3.222790607
#> [2061]  -4.481787173   8.315632397  -1.266028891   3.943316417   8.381528273
#> [2066]  -0.793030206   3.418299267   1.183296121  -1.077327611   4.400633881
#> [2071]  -2.141468293  -1.847324026   3.323493577   1.244752484   6.225683099
#> [2076]   2.317187040   3.791826068   3.791655500   3.491830255  -0.710503254
#> [2081]   1.358632508   2.996157928  -1.191287556  -0.949292260   7.574948722
#> [2086]  -4.171260964  -2.374322499   4.534451551  -1.016716912   1.279902460
#> [2091]  -3.795123349   2.402645592   1.567008920   4.875579491  -4.193380699
#> [2096]  -3.941979072  -2.261063274  -1.454691093  -1.003964477  -0.852303560
#> [2101]  -4.422111008   5.871562823  -6.728261627  -4.043695906  10.999323643
#> [2106]  -0.183059178   2.392779273   4.232317265   6.854193890  -5.924009213
#> [2111]   2.401092194   1.505042749   4.303986171  -3.681016048   0.104617752
#> [2116]  -7.112611905   8.302097055   5.647415181   1.679349463  -3.363199125
#> [2121]  -6.442964712  -1.590445938   1.365144960   7.688483128  -4.472484460
#> [2126]  -0.644832389  -1.177707100   0.027140419  -7.772527016  -0.624083979
#> [2131]   4.804905125  -9.224717253  -4.215664380   5.439074165   2.979394971
#> [2136]   1.117974557  -0.321949694  -8.531833718   1.041532131   1.060092991
#> [2141]   5.394864046   0.324845897  -3.348906879   0.377325937  -0.910426326
#> [2146]  -3.456357678   0.490069304  -4.613095113  -8.296106037   6.924921398
#> [2151]   1.907569044  -5.090202040  -4.113365812  -2.011997743  -3.309511123
#> [2156]   8.195542539   4.508705479   0.549869948  -9.468140885   9.939220478
#> [2161]   1.131975137   4.274345294   3.303329663  -1.103487199   6.846847399
#> [2166]  -1.338072647  -6.084999401  -0.856890766   4.426213096  -3.618083446
#> [2171]   9.876828766   6.819560100   0.477649047  -1.761862829   5.680740327
#> [2176]   4.512002760   3.285123379  -3.727689408   3.588453274  -2.540144319
#> [2181]  -9.224717253  -1.834497245   1.231508963  -4.508705479  -4.614432458
#> [2186]  10.729963068  -1.569353539  -6.559975277   6.549141922   9.229351879
#> [2191]   8.782238159   1.420599599  -2.129305103  -0.066397732   7.346558573
#> [2196]  -5.578101599  -2.043524608   5.737145323   2.657401545  -1.033542112
#> [2201]  10.574974603   0.208587262   1.127156503  -2.175988221   7.941232188
#> [2206]  -6.736005811 -10.969487654  -4.796879710  -1.485838360   3.606492701
#> [2211]   8.022420729  13.197614603   0.427643023   9.914209999   3.191735405
#> [2216] -10.002033233   5.143831929  -5.501579252   3.721880982  -1.338072647
#> [2221]   6.055226653   8.383079778  -8.969050510  -1.932746262   3.095492811
#> [2226]  -0.491988383   2.480304597  -9.116805518  -4.592517124   9.138468400
#> [2231]  -7.244430573   4.088366584  -5.863616502   0.328384379  -8.603277772
#> [2236]  -3.807303218  -1.115948298  -1.707417438   2.088440169  -2.792313093
#> [2241]  -3.692303347 -11.388327594   1.226874337   2.681494234  -4.088164448
#> [2246]   3.604791610  -6.973777767  -1.178661495  -5.394680038   7.304530544
#> [2251]  -6.647522410   3.184570587   5.649795196  -0.769409180  -6.118020362
#> [2256]  -5.541688202  10.338777027  -4.207743577  -2.981577980   3.978006914
#> [2261]  -5.102976284  -2.845817086  -1.714678740   3.526061563  -6.146615626
#> [2266]  -0.582020554  -0.906887844  -3.531719812   1.581301166   5.717727695
#> [2271]  -6.453465876  -3.118360161  -4.390706687  -3.187846058   3.985355152
#> [2276]   4.522836115  -7.800823671   7.652437158   2.032293527  -0.605877695
#> [2281]  -3.283003612  -3.986906803  -0.053300008   1.122720818  -2.472497170
#> [2286]   4.263500835  -1.674714837 -10.106749438   6.777532071   1.901760618
#> [2291]   1.381448726   1.250560910   9.866398235  -3.006807274   1.322229816
#> [2296]  -7.838422892   1.534488912   2.580052581   2.852377668   8.978120820
#> [2301]   7.540717415  -4.175895590  -1.262071733   9.391480471  -2.898683601
#> [2306]  -4.610383248  -5.392115866  -2.981577980  -3.485803841   6.504988996
#> [2311]  -4.689687266   2.508739999  -1.107933987   6.311656771  -3.265737318
#> [2316]   9.815829511  -0.283787786  -1.083762296   3.876290080   1.716016085
#> [2321]  -2.420410444   3.412584350   2.394698352  -1.125801030  -5.280822399
#> [2326]   0.372852921   1.260773453   0.141541877   5.851064903  -1.812213565
#> [2331]   0.389165646  10.545138614  -7.443640782  -4.590793305   1.164932856
#> [2336]  -1.320838027   2.445050007   3.240025226   3.497236199  -2.887855821
#> [2341]   4.255773330  10.587372461  -7.612918858  -4.454121195   5.400338287
#> [2346]  -9.747721963   3.968529951   0.602427974  -1.719834800  -3.269034599
#> [2351]  -2.449466645  -5.775702769  -1.417494696  -7.145314505   3.855516060
#> [2356]   2.365252189   5.907010709  -0.156140871  -0.622164900   1.404479251
#> [2361]  -4.299282728   0.310265030   2.223981658   3.122411118   1.923037025
#> [2366]   5.196296447   2.685032716  -1.338072647  -0.991137697  -4.581327047
#> [2371]  -1.269108184  -1.673161439  -6.097631069   1.777729952   1.226874337
#> [2376]  -1.356633507   2.410818700  -3.653166062   9.494495585  -0.346761231
#> [2381]   7.914865318   8.150229253   3.317041622   7.816139211  -2.522538443
#> [2386]  -3.508305510   7.892581637  -3.982639605  -0.400505901  -4.160046594
#> [2391]   9.307793305   3.166023314   0.464139224   7.941232188  -7.922855336
#> [2396]   6.547222843  -8.784421168 -10.417677643  -0.850911771   3.287836991
#> [2401]  -7.346558573   3.070681274  -2.454120317   7.170113045  -7.198436137
#> [2406]  -0.678731506   8.475267112   6.322118870  -5.084576703  -2.829880747
#> [2411]  -5.007675088  -4.464770542   5.589717035  -7.015988886  -2.494228348
#> [2416]  -2.124865589   3.415219975  -8.341051749  -0.728899153  -3.316328758
#> [2421]  -3.210969025  -2.123366622  -1.653258693   0.735855681  -0.008896592
#> [2426]  -4.352786721   5.550793909   4.301086616  -1.818665519  -1.482759068
#> [2431]  -7.580573140   1.677079519   2.236327976   5.472523051  -0.014376881
#> [2436]   0.349476778   2.468700265  -8.532550264  -2.311622300   2.856646613
#> [2441]   0.160775497  -5.626156043  -6.366154859   6.790871326   4.133741665
#> [2446]   1.748523573  -9.918844625  -4.563570994   6.175901927  -3.344396733
#> [2451]   2.424490146  -0.855748533  -3.839058287   2.770856949  -4.358788444
#> [2456]  -3.748449988  -2.067145634   3.643439556  -0.369761458  -1.801551697
#> [2461]   4.581327047   3.151695672   3.210969025  -7.348177976   3.423873066
#> [2466]   7.482376660  -1.885630981   5.345754002   1.227517865  -2.784782594
#> [2471]   2.889154101  -2.460986346  -2.177987222  -2.596345244   5.889800781
#> [2476]  -0.987660710  -0.472570754  -0.459818320  -4.016742793  -7.446339649
#> [2481]   1.230153490  -1.429892554  -0.643283619   7.918201664   2.008108396
#> [2486]   4.650492198  -1.796727456  10.480069355   2.812711675  -1.392863815
#> [2491]   5.346632158  -3.710680199  -0.739192027   1.795755791  10.028124003
#> [2496]   1.296555346  -1.392081394   6.656397608  -2.070063317  -0.729064114
#> [2501]   4.839388738  -2.305813873   9.345025099  -1.569353539  -9.541165264
#> [2506]  -2.320577829  -0.005787033  -3.003332035  -6.059861279  -6.117926853
#> [2511]  -4.784529273  -1.382379579  -0.203179913  -9.796832007   0.229365111
#> [2516]   4.406795468  -7.855809952  -1.022316638   1.228816144   1.986521199
#> [2521]  -3.619381726   8.252309833   3.880924706  -2.007269609  -0.487537176
#> [2526]  -4.593908913  -6.534561975   2.630264423   3.005749672  -1.756055819
#> [2531]   6.150884572   3.022468433  -4.894599871   5.009633245   6.447657450
#> [2536]   5.969741175   0.202814232   4.130600431   4.618701403   0.602409847
#> [2541]   1.190998935  -2.591874163  -1.127156503  -4.948392935   1.228598156
#> [2546]   2.464065639  -2.430573753   5.151622087   3.205344607  -3.228356085
#> [2551]   5.198295447  -1.371917480   3.323493577  -0.624083979   1.854425602
#> [2556]   6.370571497  -2.332088652   2.017414791   6.495043675  -7.517963440
#> [2561]  -5.759244996  -1.259801789   3.157112719   2.204077992  -7.390136789
#> [2566]   0.515466257  -0.638191739  -1.790919030  -0.239480854   2.449466645
#> [2571]  -2.346323901   8.760564027   4.616431459   4.091702930   0.988028138
#> [2576]  -7.234218030   3.953949085   1.963875401   6.054236862  -6.846847399
#> [2581]   2.489811710   3.283975277  -6.746638479  -9.201078100   2.928711466
#> [2586]  -6.319848926  -4.347369673   4.528460533  -6.814285628   0.435301011
#> [2591]   1.567008920  -0.285706865  -9.861561473  -0.428481810  -8.946766829
#> [2596]   1.482920677  -1.020985857   3.787548164  -0.140204532  -3.943316417
#> [2601]   2.216659858   9.944058159  -0.826096552  12.193917353   1.269728983
#> [2606]   5.684496797  -3.025167300   3.163988916   6.981124258   1.311767717
#> [2611]   0.086002608  -2.366608581  -3.410063915   0.136022072   0.467947232
#> [2616]  -7.025006659   3.267736319   0.750175560   1.462638333  -6.744719400
#> [2621]  -0.930892679   7.935436283  -4.316554597  -8.784421168  -8.252309833
#> [2626]   5.296483558   0.338814910   4.396364936   7.681125932   5.344362213
#> [2631]   9.944058159   0.213842699  -2.814412766   0.596784509   1.212686508
#> [2636]   1.768819357  -0.649101334  -7.006423989   4.570864948  -1.673323049
#> [2641]  -7.637340434  -5.777001049   3.142166172   2.174596433  12.943304252
#> [2646]  -7.390136789  -3.334142923   2.218279261   1.918929690  -1.729701119
#> [2651]  -1.764827340  -6.997949459   0.241289862   5.444891880  -5.502590026
#> [2656]   0.051130438   1.982713190   4.840469030  -1.462638333   6.915802694
#> [2661]  -2.449282636  -8.808592860  -1.191216923   6.558017120   1.716948684
#> [2666]  -2.733843971  -7.855809952  -5.062443381  -7.349476256   3.285123379
#> [2671] -10.777774832   4.610015821   3.588637283   0.139840787   0.872206306
#> [2676]  -4.614432458  -2.261776138   2.257765994   0.106166522  -2.902734557
#> [2681]  -0.923936150   0.257800513  -0.037558781  -6.893301025  -7.574166300
#> [2686]  -2.439764830   0.051130438  -7.566463486   0.605707127   1.163013777
#> [2691]   3.361079358  -4.671567918   3.157112719   0.619815034  -2.567080753
#> [2696]  -1.424418313   4.868743729  -2.739834989  -0.888706252   0.720023955
#> [2701]  -6.650032139   1.924554108  -5.832044523   2.251143471  -2.321088557
#> [2706] -10.172071002  -4.519167578   2.948466520   9.096429665  -0.871489760
#> [2711]   2.703409568   2.640087005   1.839150918   3.058100328   6.257037090
#> [2716]   9.802708244   2.675778397  -1.660972611  -7.121682215  -0.244680651
#> [2721]   2.045707617  -2.856817181  -1.121513038  -1.145721046   1.903300099
#> [2726]  -1.788041873  -9.722509348   2.273081534  -1.817488036  -1.846958345
#> [2731]  -2.985714875   4.258408955   7.423540110   7.977475017   2.451465646
#> [2736]   1.186582298   0.872206306   5.191661821   1.541445441  -2.463701893
#> [2741]   0.064127787  -9.228525262  -2.023769554   0.607845021  -3.542181911
#> [2746]  -3.498385707   0.372691311   3.618440328  -0.792058542  -3.516251831
#> [2751]  -5.248453805  -1.982931178   2.876860856   0.669567687   2.465402984
#> [2756]   1.440354653   1.585811312   3.459654958   1.689661385  -1.234864355
#> [2761]  -0.627001662   0.490069304   9.541360376   8.531833718  -3.763328725
#> [2766]  -2.209115442   1.271027263   3.610276019  -8.299914046   1.113339931
#> [2771]  -0.479406517  -4.786675966   4.411266549   0.854450253  -0.323467695
#> [2776]   8.247893195  -2.870834441   5.338887973   5.287376932   4.537932840
#> [2781]   1.319057015  -4.340388863  -7.827960793  -7.222973510  -4.363880324
#> [2786]  -0.696337381   0.777111994  -4.152038448   0.724611161   3.312204861
#> [2791]  -4.017123218   4.819174495  -5.078597708   2.321455985  -0.151669790
#> [2796]  -3.752718933  -8.972858519   2.051422534  -0.817783631   2.876860856
#> [2801]  -3.816868114   1.599420514  -1.259801789   3.515599464   2.787682150
#> [2806]   4.093001210  -5.601132124   1.000667197   0.923936150   3.436441491
#> [2811]   2.666196822   1.850433585  -0.548571668   6.018604967  -3.417250543
#> [2816]   5.120636443   4.803544904   5.399498672   5.521334306  -1.121365346
#> [2821]  -0.624083979   5.053373070 -11.090622116  -0.441612036   6.455821759
#> [2826]  -5.544985482  -1.492460883  -5.181199722   5.082819233   1.038195785
#> [2831]  -4.014043925  -0.619644466  -2.770856949  -7.694474146  -4.452108607
#> [2836]   3.030963206   1.605228941  -4.297984448  -3.415219975  -2.366572265
#> [2841]   1.452176235   0.399609618  -0.659413256   5.285675841   6.373989543
#> [2846]   4.650951388  -4.916056016   1.824795430   4.758599192  -7.434540205
#> [2851]   1.264254742   4.055206730   2.071982396   3.412779462  -1.224162472
#> [2856]   9.541165264  -3.224088887  -0.389165646   5.575022307  -2.034187915
#> [2861]   2.786504667  -1.630757024  -4.136396336  -1.006404990   3.693477147
#> [2866]   1.804919610   0.682608742   1.201461034  -4.971042297   0.595447164
#> [2871]  -1.423853142  -9.391480471  -6.485451930  -1.653258693   0.126492572
#> [2876]   6.042765554  -2.061946575   1.842487264  -4.232478875   1.247192997
#> [2881]   0.602409847  -3.339141295 -11.138375768   2.423191866   0.645710545
#> [2886]  -2.155887550   0.906887844   4.998604777  -0.949098962  -9.051483954
#> [2891]  -9.031383282   0.592367872   1.467272959  -2.374322499   6.209007338
#> [2896]  -0.572950243   6.618627819  -0.151875608   3.834423661   0.147022167
#> [2901]  -4.012802314  -4.214837763   0.733533779   5.590958646   6.343044412
#> [2906]  -2.800250575   3.860169732   2.852377668  -5.218823634  -4.408762794
#> [2911]  -1.534488912  -2.071616715   4.658470194   4.951931417  -1.565653448
#> [2916]   0.593264155   3.656071223  -4.703335984   5.582736225  -4.485268462
#> [2921]  -6.089630345  -9.698451518  11.336759360   4.277447462   2.474496170
#> [2926]  -7.740929518   9.944058159   8.552926117   5.759020144  -6.118020362
#> [2931]  -1.768819357   3.381375142  -2.050147130  -0.782311054   1.645432219
#> [2936]  -8.742393140   5.013333337  -9.954003480  -1.509677375  -4.056598518
#> [2941]   4.968929921  -3.975823905  -0.137764019 -12.576238364  -5.143429932
#> [2946]  -6.964395960   2.042352224  -4.469436735  -3.838690859   2.967666160
#> [2951]   0.588427393   4.044972377   3.294033973  -3.959148144  -0.996157050
#> [2956]  -2.093074795  -8.926185159   3.960337797  -6.862315380   6.675613100
#> [2961]  -3.376547339  -0.104617752  -1.351796745   1.450056467   0.240573316
#> [2966]   5.362118266  -5.313674439 -11.717782091   7.452285552  -6.135005425
#> [2971]  -4.086228690  -6.715710027  -1.759147282  -4.268354276   4.331651322
#> [2976]   3.729045800   4.522836115  -9.464722838   1.601690459  -0.722246479
#> [2981]  -0.237699841   1.205418192   4.529816925   4.453500396   7.652607727
#> [2986]  -3.372304831  -4.135039944  -2.176263402   6.848355313  -6.697333175
#> [2991]  -0.956273070  -6.006207109   4.893956343  -2.819266207  -2.788302949
#> [2996]   1.907108108  -1.239456203   8.223253632   4.336850381  -9.419145622
#> [3001]  -5.419874525   3.414171251  -8.951184386   9.186497233  -6.862936180
#> [3006]  -0.331020004   1.324531255  -0.092818307  -2.118655756  -2.761291133
#> [3011]  -7.054636831   1.233232782 -10.968395192  -4.845949319  -0.809976204
#> [3016]  -3.871854396   5.854144195   3.808703806  -5.460723607 -10.568972880
#> [3021]  -0.140204532  -6.504988996  -4.630311605   2.160120179   6.193070999
#> [3026]   8.087619554   5.317065228   2.155703541   3.286113171  -2.346105913
#> [3031]  -5.690280533  -7.538798336  -1.163013777   0.418625249  -7.591826459
#> [3036]   1.657675331  -1.246975008   6.075693006   0.622530581  -4.482189169
#> [3041]   2.258846285   3.378466418   3.752866626   5.076403595   0.352752249
#> [3046]  -7.895917983  -9.205494737   2.519441882   6.384899138   5.759020144
#> [3051]   1.306475149   2.359443762  -8.603277772  -1.008403991  -4.060717286
#> [3056]   4.673687685   6.536560975   6.055226653  -1.837794526  -6.695552163
#> [3061]   6.088274872   4.519167578   0.638639235   3.100973101  -3.793356591
#> [3066]   0.448018876   0.699433943  -2.172872613 -11.806685616   8.500204546
#> [3071]   2.275522047  -1.467054971   4.458974636   6.587883376   0.704087615
#> [3076]   1.222814421  -0.304083570  -1.044243996  -1.301840523   5.387699228
#> [3081]   4.626893558   5.054946531  -0.027140419   7.032353150  -2.311528791
#> [3086]  -4.473840852  -7.127708629  -1.437595368   2.892692583  -0.905164025
#> [3091]  -3.590556362   8.904452914   0.988867753  -2.230847687  -9.819585981
#> [3096]  -2.572876659  -8.338134066  -5.982202275   9.025507045   8.063081262
#> [3101]   4.847091552  -7.986545328   6.750595637  -1.206878082  -3.839058287
#> [3106]   5.225446156  -3.864897867   0.382159315  -5.011334336   0.054886908
#> [3111]  -4.592610633  -7.833526271   1.864345405   3.157112719   5.863616502
#> [3116]  -4.793082805  -6.065060339   3.618301434  -2.899051028   9.872194141
#> [3121]  -5.835687421   4.077733917   6.939257839   3.064090426  -8.057989382
#> [3126]  -1.244090828  -5.816776402  -1.317776862  -1.445585387  -1.364450223
#> [3131]  -3.497029315  -5.782659297   5.874278370   5.121973788   1.881362036
#> [3136] -10.036436924   2.536267083   1.714678740  -0.670924079  -7.730511157
#> [3141]  -1.481828216  -0.913084827  -3.745738124  -1.003964477  -1.969499819
#> [3146]   6.906330387  -3.434637603  -1.206971590  -1.733933748  -1.734335745
#> [3151]  -6.033288591  -6.508268149   4.038842465   0.397426609  11.908402450
#> [3156]  -4.071327077  -5.439267462  -2.625566555  -7.375843127   2.981577980
#> [3161]  -0.160775497  -4.648768379  -3.163988916   1.981539389  -1.280191082
#> [3166]  -3.558656246   4.765945683  -3.760616860  -0.994894167   6.922209533
#> [3171]  -8.783064776  -6.251264061   7.999297762   0.066397732  -2.232145967
#> [3176]  -5.942683975  -4.590793305  -2.380361911  -3.237887332   4.893956343
#> [3181]   6.506712816   5.424310209   0.735855681   7.070573170   5.685577089
#> [3186]   3.842741816   0.517883894   3.314329758   4.216175108  11.580028245
#> [3191]  -2.713158803  -0.568326721   3.938899780  -8.111476695   4.665759491
#> [3196]   0.985788460   1.569353539   1.863943409   4.400999562  -3.360417702
#> [3201]  -2.196364074  -4.364596870  -0.699433943   1.467272959  -1.931390789
#> [3206]  -5.451021792   8.863579141  -5.638712298  -1.981539389   0.914865840
#> [3211]  -3.507491414  -5.479295571  -2.494412357  -1.127138376  -4.728553199
#> [3216]  -2.465620972  14.189190096   0.530545828  -4.371226815  -1.711140258
#> [3221]  -0.281439666  -2.373955072  -9.349659725   7.559116995   2.535290878
#> [3226]  -7.477284780  -0.257582525   6.172604646  -0.796466380  -6.193070999
#> [3231]   8.956021148  10.290747275   0.830365497  -5.457621438   6.439667431
#> [3236]  -8.211010521   0.032924155   2.655564154  -1.543715385  -6.278331625
#> [3241] -10.522108089   3.178605179   4.643914937   0.516821729  -6.788872325
#> [3246]  -4.399662217   3.092780947  -5.151622087   9.006169748  -0.431544541
#> [3251]   0.325305086  -7.560472468  -9.278737104  -2.232972584  -4.714641379
#> [3256]  -0.441612036   0.683584947  -2.560308233  -1.202518637  -7.285786264
#> [3261]  -4.321014973  -1.377032089  -4.581327047   6.591180656   0.139101365
#> [3266]   3.155113718  -1.422148369   3.344178745  -5.705757682  -0.873759704
#> [3271]   7.652437158  -3.720382014   0.591908682   2.977585963   6.932819325
#> [3276]  -0.012653062   0.670924079   3.063098699   3.497236199   6.059861279
#> [3281] -13.516245622  -2.567654724  -3.670375990  -2.410359510  -0.680505655
#> [3286]   5.457255758  -1.482759068  -5.139197303  -0.986729858   4.329015697
#> [3291]   0.336815910   2.403011273  -2.216659858  -0.462001329   1.206314475
#> [3296]   3.353560552   4.581327047   3.032170248  -3.727689408   2.460986346
#> [3301]   5.164203953  -0.945794291   0.309184739  -4.363880324   0.018368898
#> [3306]  -0.683584947   9.859441706  -4.040980360  -0.877480778   5.832044523
#> [3311]  -7.928663763   5.198416214   0.746298734  -3.732963880  -3.647139647
#> [3316]  -3.555117764  -5.896378042  -0.564189826   1.600298670   1.637286038
#> [3321]  -3.085547490  -3.689006066   2.185701140   5.269218068   4.664461211
#> [3326]   2.766864932   5.118637442  -3.525843575   0.199712064   2.962373592
#> [3331]   4.685930796  -4.241192463  -1.299946135  -1.042244995   1.750054096
#> [3336]  -0.261849723   3.737034900  -2.600818260  -3.006807274  -4.083724935
#> [3341]  -1.046368893  -9.472557523  -2.008459261  -4.623539084   3.121790319
#> [3346]  -2.934720612   1.545150779  -1.689040586   1.292759507   6.326924065
#> [3351]  -0.998677485  -8.325552200  -4.281864100  -1.150431911  -3.826122433
#> [3356]  -1.945328128   3.005033125  -2.048148130   0.035469280   4.168788884
#> [3361]  -1.396934835   0.429655611  -8.809834471  -1.077327611  -1.991783500
#> [3366]  -3.478013683  -0.622894326  -4.656300624   4.859673418   1.895107944
#> [3371]  -0.114094715   0.550841612   3.037735726   3.061454801   8.734690325
#> [3376]  -5.283901692  -1.525418601  -5.224054368  -8.122300172  -1.572781950
#> [3381]  -6.278493235   9.116805518  -0.815784630   3.148157190  -8.969050510
#> [3386]   1.371917480  -4.241217154   1.987366862  -5.601958741   5.253063740
#> [3391]   6.479575693  -0.897419840  -9.075655645  -5.106055576  -2.450674425
#> [3396]   2.757701113  -0.291501704   2.538024552   5.817856694  11.394042511
#> [3401]  -0.120265470   3.143522564  -2.428539356   2.554827943   4.539288313
#> [3406]   5.309257801  -3.276167850   4.463628309   1.982252254 -10.256343584
#> [3411]  -2.670924956  -9.530532596   1.479112669  -6.741118673  -8.061907462
#> [3416]  -1.960429509  -8.621728970  -1.369281855  -5.079739941  -4.091082131
#> [3421]   6.126149274  -2.183702140  -3.650786046   0.473232410  -1.128895845
#> [3426]   4.284612281  -4.580028767   4.012802314  -8.081903717   4.544798869
#> [3431]   3.059835398  -0.512168976  -5.501579252   7.843057518   1.897106945
#> [3436]  -2.190568168  10.884065417   6.750595637   2.534888881 -11.366389531
#> [3441]   1.240672782  -7.700880986  -5.590958646   0.448202884  -6.694253883
#> [3446]   9.339912237   0.166777221   2.803618489   3.960539933  -1.184469921
#> [3451]   1.859721883  -5.207580033  -5.641642151  -8.067715888   5.439074165
#> [3456]  -4.541471322   1.527836239  -4.215126384  -1.802920610  -6.399627698
#> [3461]   4.186544937   5.741584837  -9.113875665   6.695552163  -1.413434781
#> [3466]   7.310521562  -1.054132124   1.144177882   0.119901724  -0.328384379
#> [3471]  -2.870834441   0.512534657   1.079848045   4.405435247   4.656471193
#> [3476]   0.783884515   5.582368798  -2.346105913  -0.861544439  -1.178661495
#> [3481]  -1.065736456  -3.152993951  -4.083724935  10.167440059  -4.887782236
#> [3486]   6.613003401  11.542429024  -1.083762296  -1.840488263   4.953655237
#> [3491]   2.956658674  -0.320192224   0.710642148  -7.372913274   2.696063078
#> [3496]  -0.534027117   3.880924706   1.660031213   1.901117090   5.535697184
#> [3501]   1.799632618   3.618440328  -1.876363665   3.842959804  -4.872500199
#> [3506]   9.916129078   0.950647732  -3.755982234 -10.384354244  -1.483747295
#> [3511]   3.364497404  -5.207580033   2.055862048  -0.237699841   0.793926489
#> [3516]  -0.922155138  -7.314060044   2.004351926  -7.046934017  -6.177239272
#> [3521]  -7.605763798  -1.429892554   0.268319805  -8.039589801  -6.172604646
#> [3526]   3.679842247  11.655390379   2.372598680   1.375308269  -3.535988757
#> [3531]  -2.889980718  -6.066452127  -4.173625645  -0.193708525   8.712752262
#> [3536]   0.500885390  -2.368607582  -2.424765327   7.330679427  -1.507041749
#> [3541]   3.648437927   4.843031637   1.452176235   3.384274844  -3.694525872
#> [3546]  -0.666270406   7.950904264  -4.656471193  -2.173333549  10.413921173
#> [3551]   0.998677485   2.098189404   3.303329663  -3.415219975   3.193654484
#> [3556] -11.583364591  -2.560308233   2.945138973  -1.001770364   8.363151421
#> [3561]  -1.878362665  -1.117096401  -4.458148019   4.136396336  -3.659375895
#> [3566]  -1.079108623  -2.050147130  -1.857527770   4.661951482  -3.749328144
#> [3571]   1.792310818   0.239480854   2.373955072  -0.884071626  -0.625609873
#> [3576]   4.581327047   0.622530581  -1.325705056  -0.663829894  -3.595409803
#> [3581]   5.477538102  -2.507441719  -1.270661582  -3.584747936   0.200815231
#> [3586]   5.759244996   0.984948846  -4.102947451  -9.837503644  -0.719805967
#> [3591]  -6.203349089   8.150431389   0.779047753   8.134931840   4.232111447
#> [3596]  -6.130588787   2.818369924   3.525843575  -8.815549389   0.813514686
#> [3601]   6.322484551   0.068517499  -3.526061563   5.896010614   7.498740924
#> [3606]  -1.663110506  -3.456737276 -11.481647757  -3.365071375   0.554598082
#> [3611]  -5.271440592   8.807714704   0.607062600  -3.792384926   5.927765683
#> [3616]   4.091082131  -0.752094639   6.417383751   3.901300559   1.512850176
#> [3621]  -4.268354276  -1.339616876   6.145467524  -4.590793305   9.471679367
#> [3626]  -0.886707251   4.937332423   8.972858519  -1.900036798  -3.855516060
#> [3631]  -8.475267112   6.316310444  -2.704053096  -4.152700103  -2.231215114
#> [3636]  -0.224925597   2.871052430   3.693445580   3.005033125   5.472523051
#> [3641]   6.135005425   0.410433095   1.189950211   0.548571668 -10.662516606
#> [3646]  -2.203916383   1.737047609  -3.982639605   1.924738116  -3.286113171
#> [3651]   3.100127437  -7.919499944   5.808750987   2.708063241  -3.079035038
#> [3656]   1.501756572  -3.213088792   4.725255919   2.390063726  -9.235481791
#> [3661]  -2.964493359  -1.271027263  -7.348395964  -0.261154986  -4.050572104
#> [3666]  -5.270391868   1.801381129   4.466068821 -12.003296993   2.591253364
#> [3671]   7.747336358   2.288348827   9.679114222  -4.204205096  -6.675451491
#> [3676]   7.140277055   1.568732740   0.068517499  -0.815784630  -2.408806112
#> [3681]   3.571628074  -1.587900813   9.291489539   2.969778536  -3.828058192
#> [3686]  -6.512278294  -5.256391287   3.384274844  11.090622116   1.900036798
#> [3691]   1.163013777  11.247919077   2.155703541   4.104284796   1.348906002
#> [3696]   2.067145634  -0.423847184  -0.752094639   5.282960294  -5.332712947
#> [3701]  -1.038816584  -1.779912961   2.810147503   1.965083181  -0.406382138
#> [3706]   0.671750696   5.444891880   6.399627698   4.681879839   9.186497233
#> [3711]  10.283790746  -5.063651161   5.403635567   4.495698993   6.803623760
#> [3716]  -2.910352741   1.060111119   3.264657027  -2.094798614   3.900461771
#> [3721]  -5.727615823   2.260683676  -3.191953394   2.876860856  -1.180786392
#> [3726]  -8.299914046  -1.632869400   5.538332809   3.600684275  -7.986545328
#> [3731]   5.721118484   5.783818684   3.314329758   3.406788444   3.897544089
#> [3736]   6.524099876   1.628045159   2.363322404  -2.594791846   2.118288329
#> [3741]  -2.778375755   2.915508801   8.587809791   8.976121820   2.449466645
#> [3746]   2.131294815   0.588427393   8.785776641   4.137222954   2.474496170
#> [3751]  -6.202591700   0.048860494  -0.348041383   2.744926869   0.405980141
#> [3756]   6.744197966  -2.967884148  -3.456575666  -2.140388001   3.414709247
#> [3761]  -1.692740677  -0.793030206  -1.240098811   1.038195785  -7.612918858
#> [3766]  -3.267736319  -1.733037465  -6.469515591   3.563638055   2.510738999
#> [3771]   7.700880986  -1.079326611  -5.919592575  -1.079108623  -2.538024552
#> [3776]  -2.177141558  -1.044243996   3.462545702  -1.150351989   2.220198340
#> [3781]  -1.427956795   9.915048787   5.487103917  -5.401636566   2.185701140
#> [3786]  -5.726317544  -3.904379851   0.346761231   5.126444869   7.504314723
#> [3791]   5.854362183   0.371299522  -4.408762794  -5.684278809   0.595245028
#> [3796]   1.164312057  -3.356196177  -0.318193224  -4.486605807   0.854450253
#> [3801]   1.230517235   6.331359749  -2.123366622  -6.320359654   5.142551777
#> [3806]   5.503578253   2.243014559  10.854217258 -10.476530873   9.329088760
#> [3811]  -7.983466035  -5.830689050  10.417677643  -4.219472389  -0.377107949
#> [3816]   6.459411780  -1.497121946  -1.334993354  -5.854546192  -4.361881323
#> [3821]   0.844553326 -11.330352520  -1.729701119   0.680851273   6.633585072
#> [3826] -11.074685777   2.664495731   5.037541344  11.414418364   5.873561823
#> [3831]  -5.457473746  -3.309331386  -0.123383013  -0.926476041  -0.929191588
#> [3836]   3.270371944  -6.322484551  -5.730971216   2.096797615   8.803958234
#> [3841]   2.617437643   9.976819699   2.096797615   4.996605777  -5.822567559
#> [3846]   2.242136403   3.545059067   6.319848926   3.901082571  -7.816484829
#> [3851]   7.358608507   7.833308283  -4.545879160  -2.167525123   2.895753748
#> [3856]   6.634941464   2.071798387  11.084745879   6.935339759  -0.894707975
#> [3861]   0.618057565   9.976819699  -5.138990419  -1.419436504  -1.184687909
#> [3866]   0.703869627  -4.107364088  -3.749421653  -5.759020144  -2.930089668
#> [3871]   8.442930193  -7.501141922   1.979419622   4.508705479   0.461059931
#> [3876]   7.935436283   0.574135148  -2.975586962  -3.733698553  -0.346743104
#> [3881]  -2.739639877   0.963229598  -2.597061790  -2.366608581  -2.909507078
#> [3886]   6.937258838  -6.712600468  -2.580236589   2.082461174  -5.414053928
#> [3891]   4.347771670   4.389810404  -3.757981235   0.474569755   1.224162472
#> [3896]   3.122065500   0.032924155  -2.875023465   4.266216382  -0.179141098
#> [3901]   8.783064776   2.724171895   4.268354276   0.726002949  -1.245894717
#> [3906]   8.233141760   1.615038673   1.484540080   1.924738116   5.345660493
#> [3911]  -0.783884515  -3.762615861   1.060092991 -10.067231138   5.643986770
#> [3916]  -1.859721883   4.346032328  -6.603150669   8.247893195  -3.019358874
#> [3921]  -0.514088055  -4.447691969   4.861672419   0.369979446   4.182330275
#> [3926]   4.451230451   1.279902460  -6.088090863  -1.576079231  -0.055954679
#> [3931]  -0.896488988  -1.779912961  -1.152350990  12.443593078  -3.235888331
#> [3936]   4.285345389   7.032353150   4.747568831  -6.253681698   3.535017092
#> [3941]   6.889872614  -4.146323530  -5.009996990  -5.873561823  -0.764755507
#> [3946]  -2.589754396  -1.695261112   4.914354925  -1.610931337 -11.770648605
#> [3951]   3.674277507   5.999371347  -8.897496385  -1.030462820  -2.535106869
#> [3956]  -0.032948846  -6.084999401  -2.911712963   3.211153034   1.860864116
#> [3961]  -7.697951133  -0.437195399  -6.061981046  -7.006262380  -3.690935851
#> [3966]  -4.279865100   2.847941983  -5.922928921   3.125340971  -7.064914921
#> [3971]   2.102927527  -1.383206196   1.616739764   0.193708525  -4.074624358
#> [3976]   5.384401947   7.652437158   4.999961169 -10.663814886  -4.781413664
#> [3981]  -5.357264825   7.786854658  -1.419243207   3.956068852  -0.096626316
#> [3986]  -2.236562604  -3.417218976  -7.855809952   1.657893319  -1.938684743
#> [3991]  -4.129302151  -0.802882019   1.878362665  -1.205418192   1.660972611
#> [3996]  -1.764827340   2.236327976   0.357951308  -4.778527549   2.854898102
#> [4001]  -8.223471620  -2.763326450   5.006917698   0.051301007   4.842870027
#> [4006]   3.110589536  -0.682149553  -0.934794196  -5.267219067   6.252803542
#> [4011]   1.795755791   4.449393060   1.712648172  -4.418464609  -5.387481240
#> [4016]   7.537178933  -0.852085572   1.077407532   3.846223105  -6.133863192
#> [4021]  -0.963229598  -3.404789444  -2.522709012  -1.914915535  -4.889325399
#> [4026]   1.759353100   0.084453838  -1.151730191  -0.474601322   3.731410482
#> [4031]   9.274102478  -6.465413503   0.647893554  -1.781085344   5.982202275
#> [4036]   7.015988886   2.468700265   1.570364313  -3.710462211   2.407280218
#> [4041]  -1.128895845  -8.693334634   5.565199726   5.529106336  -0.619894956
#> [4046]   1.338594080   0.076525645  -7.075748277  -8.399904978  -5.479295571
#> [4051]  -2.177987222  -0.861544439  -1.089570722  -0.445123592  -1.207337271
#> [4056]   1.621593205   0.038950569  -2.847576302   4.036843464  -4.156967302
#> [4061]  -4.168168085  -4.859673418  -1.292965325   1.977420622  -0.666270406
#> [4066]   2.073981396  -3.431219556  -2.478603506  -1.733055592  -8.299914046
#> [4071]  -7.112611905   2.930089668   4.875579491  -7.446720074   4.389408408
#> [4076]  -7.123439684   7.448477543   0.839721694  -0.796327487   6.193070999
#> [4081]   0.988867753  -1.795755791   2.724171895  -3.691446579   1.865530309
#> [4086]  -3.605871902   0.969852121   0.678731506   0.399425609  -2.238768489
#> [4091]  -6.018604967   5.211047881  -0.305887458   5.161662656  -6.215009061
#> [4096]  11.908402450   2.358687778   1.716016085  -6.114847561   5.335406684
#> [4101]  -5.609134663 -10.227057284   2.697430574 -10.109464985   3.279247142
#> [4106]  -4.791083805  -4.681879839  -7.493221119   2.332088652  -0.620182462
#> [4111]   1.123782983  -3.381375142  -6.319848926   2.230847687   3.614032489
#> [4116]   0.854450253   1.785501982  -5.477940098   7.611702279   7.858889245
#> [4121]  -3.708761120   2.829710179  -8.078365235  -2.894416402   3.752718933
#> [4126]  -7.727799292  -6.320359654   7.304530544   0.624083979  -2.375954072
#> [4131] -10.401168739  -7.881338036   5.808630221  -8.121422017  -2.856817181
#> [4136]   5.694088541   0.141759866  -2.479533620  -0.920856858  -7.444939061
#> [4141]   6.133863192  -3.795193982  -3.687649674   6.046062834   4.784529273
#> [4146]   4.720437285   5.031732917  -7.185854272  -1.962153329   1.726414942
#> [4151]   0.859650050  -1.807360123  -4.656471193  -0.836330905  -4.480797381
#> [4156]  -5.224985220   2.555837152   1.712477603  -1.677079519  -3.513287319
#> [4161]   2.737119442   8.360072129   0.627001662  -4.898225288   6.249047072
#> [4166]   2.630264423   4.556091704  -2.435009438   2.899051028  -2.172872613
#> [4171]  -1.700079746   4.361881323   4.642361539  -1.938684743   0.133839063
#> [4176]  -6.501450514   9.616504522  -3.434637603   3.033927717   1.848295690
#> [4181]   2.100901268  -8.262771932  -4.597447395  -0.134684727  -1.786284404
#> [4186]   0.649285343  -3.165380705  -7.393473135   2.185333713  -3.191213972
#> [4191]  -0.516821729  -4.255773330   1.842487264   8.549589771  -6.395927606
#> [4196]  -3.795100473  -4.961001727  -0.977028043  -2.964493359   1.163013777
#> [4201]   0.183059178  -5.594255927  -5.113983769  -2.497514525  -4.746712063
#> [4206]   3.206316272   6.820081534   4.321841590   5.393472258  -5.384401947
#> [4211]  -5.143613941   2.609630216   0.622164900  -3.808703806  -2.622091315
#> [4216]  -1.044243996   3.495030314   1.072554091   3.956068852  -6.450129530
#> [4221]  -1.545334788  -6.739762281   0.240779133  -4.790003513  -3.963876279
#> [4226]  -2.477413853  -4.613095113   0.980314220  -5.248647102   0.958192149
#> [4231]   3.896665933  -2.163406355   1.446665678  -0.913723607   1.902454435
#> [4236]   3.481387203  -2.627749564  -3.251629558   2.241847782   9.355179530
#> [4241]  -0.429274596  -4.607877926 -10.193733884   4.232111447  -0.534208789
#> [4246]  -5.944385066  -0.246575039  -9.074777489  -2.824084842  -6.112211935
#> [4251]   1.421137595   7.983466035   5.078597708  -6.130588787  -3.064872848
#> [4256]   2.763326450   5.206608368  -0.009480261  -8.879320368  -6.462697956
#> [4261]   2.737119442  -2.972494083  -0.644630253  -5.457255758   3.038161266
#> [4266]  -0.034497616   1.501756572  -2.310230511   2.182403860   3.363199125
#> [4271]  10.256343584  -3.943339293  -5.841793757   3.226598616   4.543407080
#> [4276]  -2.371623632   4.146689211   4.012802314  -2.449466645   7.891501345
#> [4281]   1.505042749   3.821303799  -0.651221101   2.845306358   6.518900816
#> [4286]   1.232354626  -0.293055102  -2.085728304   5.520036026  -6.888884387
#> [4291]   4.840469030   3.225426232  -0.855748533   8.415172271  -2.176630830
#> [4296]  -4.289246907  -1.600298670   2.042352224  -4.930016083   5.815586750
#> [4301]   0.682149553   3.944419585  -0.534027117   1.907739612  -0.740272319
#> [4306] -10.317124851   4.485066326  -4.468044946  -1.340513159  -5.986618912
#> [4311] -10.475652717  -0.543097427   8.499124254  -4.482946559   4.071327077
#> [4316]   2.109550049   3.554899776   1.051350702   1.978203043   5.838402968
#> [4321]  12.194997645   4.744489539  -4.640013420   2.889154101  -0.897419840
#> [4326]   1.211606216  -0.819966640   7.752449220  -1.440892648  -4.093644738
#> [4331]   1.807360123  -2.908610794   2.677134789  -6.814285628   7.922211808
#> [4336]  -6.746638479   1.358632508  12.802895735   2.782494523  -0.681585946
#> [4341]   1.589108593   2.626507953  -7.372035118  -1.105038703   3.797113061
#> [4346]  -2.421468046   2.763326450  -1.181758057  -6.397481004   1.207153263
#> [4351]  -0.656057863   7.309223282   4.016742793  -2.697430574   0.401747512
#> [4356]  -7.169286428  -2.860924517   4.150976284   0.067639343  -2.374322499
#> [4361]  -4.630311605   1.036897505   0.003088165  -2.897752748  -9.088116745
#> [4366]  11.277486006   2.130835625  -4.702623119  -6.456763157   2.070224926
#> [4371]   8.745983160   1.706486585  -0.812785260   3.152993951  -2.012561349
#> [4376]   3.443801422   1.804919610  10.680692624   1.881362036  -2.127819575
#> [4381]  -5.663741824   2.580236589  -0.586491635   8.512254480   2.991523302
#> [4386]   4.804905125   3.533868990  -5.602469469   0.193708525   4.276275079
#> [4391]  -2.899051028  -1.075570141  -6.954694145  -6.978194405   1.339214880
#> [4396]   2.622456996  -7.663270514   6.807329099   0.206806249   5.960264212
#> [4401] -11.015259982  -3.683233037   1.100587496  -2.051227422   6.639358101
#> [4406]  -0.399207621  -3.978168524   8.559119271  -6.702898653  -4.703335984
#> [4411]  -4.316384029   5.464028278   3.059455800   4.223010871  -4.478311933
#> [4416]   7.135642429   0.116565378   3.228781625   4.133110160   0.537381591
#> [4421]   8.791778365  -0.494883667   6.479575693   5.651173398   5.982202275
#> [4426]   4.654248668   1.287485036  -8.544069966   1.190998935   0.137764019
#> [4431]  11.086865646   7.222973510   0.441612036  -5.836679149   7.202852775
#> [4436]   4.319922511   0.779231761  -0.980314220  -0.847188951   4.642361539
#> [4441]  -0.452856557  -4.321220791  -5.108175343  -7.730878585   0.271380970
#> [4446]  -5.142551777   0.467436504  -0.266928016  -0.918163120  -3.338979685
#> [4451]  -4.541408080   8.016582152   0.978957828   1.593927227  -5.207598160
#> [4456]  -0.577410619   2.420628432   4.235408728  -0.019011507   8.630214206
#> [4461]   6.431964617  -5.142092587   6.735127655  -4.862752711  -3.122411118
#> [4466]   2.317039347   4.131960652   1.515866226   3.365897992  -3.286113171
#> [4471]   4.727393813   2.984657273  -3.871636407   0.574135148  -1.690182819
#> [4476]  -3.922561444  -2.856279185  -0.411789487  -0.984730858  -0.970748404
#> [4481]   7.198801818  -2.975586962  -5.196296447  -3.943121305  -6.732989761
#> [4486]   2.259064273   3.663815408   2.068903103   3.781176721   2.342751439
#> [4491]   0.602409847   6.699968800  -9.093774994  -2.580684086   0.833903979
#> [4496]  -5.015988008  -4.889325399  -0.710503254  -2.291521628  -8.744902869
#> [4501]   1.545150779   1.313576725   4.581947846  -0.125520908  -2.738091107
#> [4506]  -3.813477325   4.182330275   0.327745599  -2.600818260   7.677850461
#> [4511]   2.088658157   2.330169573   0.609182367   5.702678390  -1.687742306
#> [4516]  -8.134931840   0.278153490   8.250528821  -1.200380742  -1.098863677
#> [4521]  -8.490316417  -1.993540969  -8.308503894  -0.627001662  -0.576029536
#> [4526]   3.963876279  -4.265244717  -5.812141776   7.285786264   2.894029928
#> [4531]  -6.456763157   4.238113171   4.847286665   3.670886718   3.456737276
#> [4536]  -0.554380094   2.097510479   5.947682346   4.316554597  -1.673541037
#> [4541]   2.744306070   5.643365971   9.664534274  -5.749348068   4.394043034
#> [4546]  -3.850360000  -7.172824910   1.148996517   5.694740908   4.803715473
#> [4551]   3.648531436   2.331918084   0.148194551   1.064344667   2.849114367
#> [4556]  -0.096464707   1.520979088  -0.051301007   0.327745599  -0.140399644
#> [4561]  -9.153048347   7.398126807  -7.012450404  -2.751439321   8.468860273
#> [4566]   6.544507296  -1.974784996   4.475232640   0.187912619   7.504314723
#> [4571]   6.029023328   5.663523835  -0.477649047   0.111911706   2.190568168
#> [4576]   2.099509480  -4.203422674  -7.266368636  -1.731700119   2.535290878
#> [4581]  -3.562557763  -0.847188951  -2.559462569  -0.707787707  -4.867387337
#> [4586]  -8.160861920   8.486094892   8.249230541   5.006917698  -7.067034688
#> [4591]  -0.241921366   0.638639235   8.559119271   8.453392292   4.788229364
#> [4596]   3.535988757   0.477487438   0.348041383   6.325004986  -3.863708214
#> [4601]   2.935088039 -13.249182837  -0.661683200  -5.533916171   1.009760383
#> [4606]  -7.042299391   2.145241442  -1.437424800  -2.961075312  -1.545552776
#> [4611]   0.850911771  -5.896010614   1.203580801   0.339895202   0.406164150
#> [4616]  -6.999868538   0.794328486  -3.036437446  -4.023149632  -0.593246028
#> [4621]   0.898757185  10.141085358 -11.908402450  -7.610203311  -1.370580135
#> [4626]   0.956638750   1.792458511   0.706799480   2.508739999   2.390063726
#> [4631]  -8.169451769   8.155066015  -2.204077992   4.973757844  -4.093001210
#> [4636]  11.481647757   0.665221682   2.607189703   3.735818321 -11.717782091
#> [4641]   4.028922662  -3.590556362   1.823296463   7.448477543  -6.817561099
#> [4646]  -1.613646884  -5.520036026  -2.405361139   2.140388001  -6.353693759
#> [4651]  -4.914136937  -3.821285671   2.215106460  -3.282758698  -3.147279034
#> [4656]   2.404171486   0.723103247   8.423762120  -2.555045931  -9.981450643
#> [4661]   4.954646964   3.529600045   5.749348068   1.236162635  -5.316386304
#> [4666]  -1.423853142   1.587555195  -9.976819699   9.554389738  -9.663177882
#> [4671]   2.553654143  -0.458664983   2.230847687  -2.670304157  -5.313674439
#> [4676]  -4.038842465   2.651606706   9.159039365  10.667353368   9.584019910
#> [4681]   4.522836115   5.832044523 -12.385618004   0.961730630  -5.143613941
#> [4686]   2.622917932   0.665221682  -2.975586962   5.838035541   2.770856949
#> [4691]  -8.868671021   6.501450514  -7.537178933   1.122720818   4.088366584
#> [4696]   2.975586962  -8.230210161   3.826122433  -6.297910863  -1.364634231
#> [4701]   1.337433867   2.931629149  -5.663925832   5.332712947   1.232865355
#> [4706]  -0.321123077   6.469113595   6.524099876  -0.235942372  -1.630975012
#> [4711]  -0.646952156  -2.038089433  -8.473147345   2.661198450   2.684848708
#> [4716]  -1.488729104  -7.044814250   1.732416666  -2.120012148   6.367235150
#> [4721]  -8.480103874  -2.846184514   1.227092325   5.502751636   0.741461972
#> [4726]   0.383514788  -1.440892648  -0.460966423   1.516325415   5.874899169
#> [4731]  -2.038089433  -3.158193011   0.769409180  -2.084380253  -7.231678139
#> [4736]   9.976819699  -2.301160201  -1.885881471  10.532935869   6.922209533
#> [4741]   5.844442380 -10.052181833  -2.235482313  -3.371843895  -4.255693408
#> [4746]   5.005676087   1.450177234  -4.935995078   1.586029300   8.994796582
#> [4751]  -3.424383794   4.870742729   3.831344368   4.671052059  -5.963802694
#> [4756]  -8.968419005   9.557101603  -4.337840173  -3.981086207  -0.043598193
#> [4761]  -4.493258480   3.812139980  -0.609245609 -11.196350842   6.584773817
#> [4766]   6.319848926   3.781176721   4.137222954   8.431108611  -2.478603506
#> [4771]  -0.956273070  -4.544580881   6.657952942  -2.194351486 -11.084745879
#> [4776] -12.334049770  -3.901484567   8.338134066  -1.712477603  -1.843785544
#> [4781] -10.337478747   1.186411729  -4.012802314  -5.153892031   1.565435460
#> [4786]  -2.168040981 -12.137714493   9.204616581  -4.931353428   1.786284404
#> [4791]   7.958730738  -0.720023955  -3.769717437  -8.503540892   3.481387203
#> [4796]  -4.168788884  -1.453933704  -5.898297121  -0.348098576   9.276222245
#> [4801]  -6.880170799  -1.145721046 -10.404730096  10.180192493   2.032464096
#> [4806]  -3.465450864  -2.680777688  -1.371917480 -10.946675117   4.016742793
#> [4811]  -4.182330275  -2.478751198   4.829807162   6.589181656   3.456737276
#> [4816]   7.243919845   2.655564154   8.478805594   3.543060067  -0.343588430
#> [4821]  -1.454691093   9.494289767   3.315686150  -4.278784808  -8.433228378
#> [4826]  -0.023843139   0.808677924  -1.889299518   0.312384797  -1.324531255
#> [4831]   0.290509977  -5.118637442  -7.143540356   3.261301634  -1.264853155
#> [4836]  -4.046136419  -2.841767876  -7.123439684  -0.228004890  -0.867951278
#> [4841]   2.513432737   1.145515228  -4.094818538   3.823423566   1.000885185
#> [4846]   0.917501465   7.907162503  -5.400338287  -6.030209298   8.321634120
#> [4851]   3.598765196   3.647139647   8.003003101   4.011924158   1.609838875
#> [4856]   3.059455800  -1.234624571   3.737817321  -0.084453838  -6.676786901
#> [4861]  -5.084117513   2.271307385  -4.675686685   7.320466883  -3.007748672
#> [4866]   6.373989543  -5.286021459   2.098189404   2.743007790   5.641642151
#> [4871]   5.207580033   3.617142048   0.850911771  -1.558270641   5.562269873
#> [4876]  -9.934803840   2.635268370 -10.476530873   5.499660173  -2.966492360
#> [4881]   2.055324052  -0.224925597  10.884065417   3.077115959  -2.557022056
#> [4886]  -2.591712553   2.888050933  -2.097728467  -1.075570141   4.600495120
#> [4891]   4.118000438   0.160775497   9.141804746   6.193070999   4.358788444
#> [4896]   4.260407956  11.107447317  -1.590464985  -5.728953169   5.139013295
#> [4901]   7.888571492   2.510077344   4.883323676   1.584637512  -2.359443762
#> [4906]   4.279630472  -3.853075547  -0.769409180  -5.269000080   6.200453805
#> [4911]   3.987112621   2.490638327  -6.393969449   5.198416214   3.062018407
#> [4916]  -2.905090440  -8.386162899  -2.620918932  -1.192390724   0.124372805
#> [4921]   9.109459027  -0.002707740  -5.307959522   1.376814101  -7.079872174
#> [4926]   3.679842247   0.068517499  -0.881933731   4.235592736   1.837427098
#> [4931]   1.337877534  -0.142398645  -2.577293296  -1.147259110   1.383206196
#> [4936]  -3.541997902   3.237519904   2.357331386  -2.870834441  -1.924738116
#> [4941]   3.177415527  -1.413956214   0.980314220  -1.097508204  -5.604500037
#> [4946]   6.066817808   2.350924547  -2.688134884  -6.252344352   1.547069858
#> [4951]  -3.526682362   0.749654126  -7.352812602  -6.203533098   3.220791607
#> [4956]   4.205744577   3.303329663  -3.059617410  -2.792956621   4.443038297
#> [4961]  -3.826720846  -2.152773688  -1.690377931   0.454193902  -6.278711223
#> [4966]  -3.030389235  -2.475212717  -7.580757148  -3.005033125  -3.341099452
#> [4971]  -2.452763925  -7.261193530  -1.737874226  -3.842959804   0.999329851
#> [4976]   1.947848562   8.828010488  -8.315632397   2.967666160   4.728151203
#> [4981]   4.728335211   4.330095988  -6.783157408  -8.213041089   7.054636831
#> [4986]   2.760210842   3.365713983   1.146813507   2.200780712  -4.179250983
#> [4991]   6.887527995   0.871489760   7.727799292  -2.420410444  -1.430076562
#> [4996]  -0.042425809  -3.055200772  -1.804919610  -4.422272618   5.102976284
#> 
#> $exact
#> [1] FALSE
#> 
#> $seed
#> [1] 542
#> 
#> attr(,"class")
#> [1] "permutationTest"

  #Results of Hypothesis Test
  #--------------------------
  #
  #Null Hypothesis:                 Mean (Median) = 4.60517
  #
  #Alternative Hypothesis:          True Mean (Median) is greater than 4.60517
  #
  #Test Name:                       One-Sample Permutation Test
  #                                 (Based on Sampling
  #                                 Permutation Distribution
  #                                 5000 Times)
  #
  #Estimated Parameter(s):          Mean = 4.378636
  #
  #Data:                            log(EPA.92d.chromium.vec)
  #
  #Sample Size:                     15
  #
  #Test Statistic:                  Sum(x - 4.60517) = -3.398017
  #
  #P-value:                         0.7598


  # Plot the results of the test 
  #-----------------------------
  dev.new()
  plot(test.list)

  #----------

  # Clean up
  #---------
  rm(test.list)
  graphics.off()