Plots for a Sampling Design Based on a Prediction Interval for the Next \(k\) Observations from a Normal Distribution

Create plots involving sample size, number of future observations, half-width, estimated standard deviation, and confidence level for a prediction interval for the next \(k\) observations from a normal distribution.

plotPredIntNormDesign(x.var = "n", y.var = "half.width", range.x.var = NULL, 
    n = 25, k = 1, n.mean = 1, half.width = 4 * sigma.hat, sigma.hat = 1, 
    method = "Bonferroni", conf.level = 0.95, round.up = FALSE, n.max = 5000, 
    tol = 1e-07, maxiter = 1000, plot.it = TRUE, add = FALSE, n.points = 100, 
    plot.col = "black", plot.lwd = 3 * par("cex"), plot.lty = 1, 
    digits = .Options$digits, cex.main = par("cex"), ..., main = NULL, 
    xlab = NULL, ylab = NULL, type = "l")

Arguments

x.var: character string indicating what variable to use for the x-axis. Possible values are "n" (sample size; the default), "half.width" (the half-width of the confidence interval), "k" (number of future observations or averages), "sigma.hat" (the estimated standard deviation), and "conf.level" (the confidence level).
y.var: character string indicating what variable to use for the y-axis. Possible values are "half.width" (the half-width of the confidence interval; the default), and "n" (sample size).
range.x.var: numeric vector of length 2 indicating the range of the x-variable to use for the plot. The default value depends on the value of x.var. When x.var="n" the default value is c(2,50). When x.var="half.width" the default value is c(2.5 * sigma.hat, 4 * sigma.hat). When x.var="k" the default value is c(1, 20). When x.var="sigma.hat", the default value is c(0.1, 2). When x.var="conf.level", the default value is c(0.5, 0.99).
n: positive integer greater than 1 indicating the sample size upon which the prediction interval is based. The default value is n=25. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are not allowed.
k: positive integer specifying the number of future observations or averages the prediction interval should contain with confidence level conf.level. The default value is k=1. This argument is ignored if x.var="k".
n.mean: positive integer specifying the sample size associated with the \(k\) future averages. The default value is n.mean=1 (i.e., individual observations). Note that all future averages must be based on the same sample size.
half.width: positive scalar indicating the half-widths of the prediction interval. The default value is half.width=4*sigma.hat. This argument is ignored if either x.var="half.width" or y.var="half.width".
sigma.hat: numeric scalar specifying the value of the estimated standard deviation. The default value is sigma.hat=1. This argument is ignored if x.var="sigma.hat".
method: character string specifying the method to use if the number of future observations (k) is greater than 1. The possible values are method="Bonferroni" (approximate method based on Bonferonni inequality; the default), and
method="exact" (exact method due to Dunnett, 1955). This argument is ignored if k=1.
conf.level: numeric scalar between 0 and 1 indicating the confidence level of the prediction interval. The default value is conf.level=0.95.
round.up: for the case when y.var="n", logical scalar indicating whether to round up the values of the computed sample sizes to the next smallest integer. The default value is round.up=TRUE.
n.max: for the case when y.var="n", the maximum possible sample size. The default value is n.max=5000.
tol: numeric scalar indicating the tolerance to use in the uniroot search algorithm. The default value is tol=1e-7.
maxiter: positive integer indicating the maximum number of iterations to use in the uniroot search algorithm. The default value is maxiter=1000.
plot.it: a logical scalar indicating whether to create a plot or add to the existing plot (see explanation of the argument add below) on the current graphics device. If plot.it=FALSE, no plot is produced, but a list of (x,y) values is returned (see the section VALUE). The default value is plot.it=TRUE.
add: a logical scalar indicating whether to add the design plot to the existing plot (add=TRUE), or to create a plot from scratch (add=FALSE). The default value is add=FALSE. This argument is ignored if plot.it=FALSE.
n.points: a numeric scalar specifying how many (x,y) pairs to use to produce the plot. There are n.points x-values evenly spaced between range.x.var[1] and
range.x.var[2]. The default value is n.points=100.
plot.col: a numeric scalar or character string determining the color of the plotted line or points. The default value is plot.col="black". See the entry for col in the help file for par for more information.
plot.lwd: a numeric scalar determining the width of the plotted line. The default value is 3*par("cex"). See the entry for lwd in the help file for par for more information.
plot.lty: a numeric scalar determining the line type of the plotted line. The default value is plot.lty=1. See the entry for lty in the help file for par for more information.
digits: a scalar indicating how many significant digits to print out on the plot. The default value is the current setting of options("digits").
cex.main, main, xlab, ylab, type, ...: additional graphical parameters (see par).

Details

See the help files for predIntNorm, predIntNormK, predIntNormHalfWidth, and predIntNormN for information on how to compute a prediction interval for the next \(k\) observations or averages from a normal distribution, how the half-width is computed when other quantities are fixed, and how the sample size is computed when other quantities are fixed.

Value

plotPredIntNormDesign invisibly returns a list with components:

x.var: x-coordinates of points that have been or would have been plotted.
y.var: y-coordinates of points that have been or would have been plotted.

References

See the help file for predIntNorm.

Author

Steven P. Millard (EnvStats@ProbStatInfo.com)

Note