plotPredIntNparSimultaneousDesign.RdCreate plots involving sample size (\(n\)), number of future observations (\(m\)), minimum number of future observations the interval should contain (\(k\)), number of future sampling occasions (\(r\)), and confidence level \((1-\alpha)\) for a simultaneous nonparametric prediction interval.
plotPredIntNparSimultaneousDesign(x.var = "n", y.var = "conf.level",
range.x.var = NULL, n = max(25, lpl.rank + n.plus.one.minus.upl.rank + 1),
n.median = 1, k = 1, m = ifelse(x.var == "k", ceiling(max.x), 1), r = 2,
rule = "k.of.m", conf.level = 0.95, pi.type = "upper",
lpl.rank = ifelse(pi.type == "upper", 0, 1),
n.plus.one.minus.upl.rank = ifelse(pi.type == "lower", 0, 1), n.max = 5000,
maxiter = 1000, integrate.args.list = NULL, 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")character string indicating what variable to use for the x-axis.
Possible values are "n" (sample size; the default),
"conf.level" (the confidence level), "k" (minimum number of
future observations the interval should contain), "m" (number of
future observations), and "r" (number of future sampling occasions).
character string indicating what variable to use for the y-axis.
Possible values are "conf.level" (confidence level; the default), and
"n" (sample size).
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="conf.level", the default value is c(0.5, 0.99).
When x.var="k", x.var="m", or x.var="r", the default value
is c(1, 20).
numeric scalar indicating the sample size. The default value is max(25, lpl.rank + n.plus.one.minus.upl.rank + 1).
Missing (NA), undefined (NaN), and infinite (Inf, -Inf)
values are not allowed.
This argument is ignored if either x.var="n" or y.var="n".
positive odd integer specifying the sample size associated with the future medians.
The default value is n.median=1 (i.e., individual observations). Note that
all future medians must be based on the same sample size.
for the \(k\)-of-\(m\) rule (rule="k.of.m"), a positive integer
specifying the minimum number of observations (or medians) out of \(m\)
observations (or medians) (all obtained on one future sampling “occassion”)
the prediction interval should contain.
The default value is k=1. This argument is ignored when the argument
rule is not equal to "k.of.m".
positive integer specifying the maximum number of future observations (or
medians) on one future sampling “occasion”.
The default value is m=2, except when rule="Modified.CA", in which
case this argument is ignored and m is automatically set equal to 4.
positive integer specifying the number of future sampling “occasions”.
The default value is r=1.
character string specifying which rule to use. The possible values are
"k.of.m" (\(k\)-of-\(m\) rule; the default), "CA" (California rule),
and "Modified.CA" (modified California rule).
See the DETAILS section below for more information.
numeric scalar between 0 and 1 indicating the confidence level
associated with the prediction interval. The default value is
conf.level=0.95.
character string indicating what kind of prediction interval to compute.
The possible values are "upper" (the default) and "lower".
non-negative integer indicating the rank of the order statistic to use for
the lower bound of the prediction interval. If pi.type="lower", the
default value is lpl.rank=1 (implying the minimum value is used as the
lower bound of the prediction interval). If pi.type="upper", this
argument is set equal to 0.
non-negative integer related to the rank of the order statistic to use for
the upper bound of the prediction interval. A value of
n.plus.one.minus.upl.rank=1 (the default) means use the
first largest value, and in general a value of n.plus.one.minus.upl.rank=\(i\) means use the \(i\)'th largest value.
If pi.type="lower", this argument is set equal to 0.
numeric scalar indicating the maximum sample size to consider when y.var="n".
This argument is used in the search algorithm to determine the required sample size.
The default value is n.max=5000.
positive integer indicating the maximum number of iterations to use in the
uniroot search algorithm when y.var="n". The default value is
maxiter=1000.
list of arguments to supply to the integrate function. The default
value is NULL.
a logical scalar indicating whether to create a plot or add to the
existing plot (see add) on the current graphics device. If
plot.it=FALSE, no plot is produced, but a list of (x,y) values
is returned (see VALUE). The default value is plot.it=TRUE.
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.
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.
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.
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.
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.
a scalar indicating how many significant digits to print out on the plot. The default
value is the current setting of options("digits").
additional graphical parameters (see par).
See the help file for predIntNparSimultaneous,
predIntNparSimultaneousConfLevel, and predIntNparSimultaneousN for information on how to compute a
simultaneous nonparametric prediction interval, how the confidence level
is computed when other quantities are fixed, and how the sample size is
computed when other quantities are fixed.
plotPredIntNparSimultaneousDesign invisibly returns a list with components
x.var and y.var, giving coordinates of the points that
have been or would have been plotted.
See the help file for predIntNparSimultaneous.
See the help file for predIntNparSimultaneous.
# For the 1-of-3 rule with r=20 future sampling occasions, look at the
# relationship between confidence level and sample size for a one-sided
# upper simultaneous nonparametric prediction interval.
dev.new()
plotPredIntNparSimultaneousDesign(k = 1, m = 3, r = 20, range.x.var = c(2, 20))
#==========
# Plot confidence level vs. sample size for various values of number of
# future sampling occasions (r):
dev.new()
plotPredIntNparSimultaneousDesign(m = 3, r = 10, rule = "CA",
ylim = c(0, 1), main = "")
plotPredIntNparSimultaneousDesign(m = 3, r = 20, rule = "CA", add = TRUE,
plot.col = "red")
plotPredIntNparSimultaneousDesign(m = 3, r = 30, rule = "CA", add = TRUE,
plot.col = "blue")
legend("bottomright", c("r=10", "r=20", "r=30"), lty = 1, lwd = 3 * par("cex"),
col = c("black", "red", "blue"), bty = "n")
title(main = paste("Confidence Level vs. Sample Size for Simultaneous",
"Nonparametric PI with Various Values of r", sep="\n"))
#==========
# Modifying Example 19-5 of USEPA (2009, p. 19-33), plot confidence level
# versus sample size (number of background observations requried) for
# a 1-of-3 plan assuming r = 10 compliance wells (future sampling occasions).
dev.new()
plotPredIntNparSimultaneousDesign(k = 1, m = 3, r = 10, rule = "k.of.m")
#==========
# Clean up
#---------
graphics.off()