illustrateLLN {distrTeach}R Documentation

Functions for Illustrating the LLN

Description

Functions for generating a sequence of plots of randomly generated replicates of arithmetic means for sums of iid r.v. distributed according to a prescribed discrete or absolutely continuous distribution. A line for the expectation and CLT based (pointwise) 95%-confidence bands are also plotted and the empirical coverage of this band by the replicated plotted so far is indicated.

Usage

illustrateLLN(Distr = Norm(),n = c(1,3,5,10,25,50,100,500,1000,10000), 
            m = 50, step = 1, sleep = 0, withConf = TRUE, 
            withCover = (length(n)<=12), withEline = TRUE, withLegend = TRUE,
            CLTorCheb = "CLT",  coverage = 0.95, ...,  col.Eline = "blue", 
            lwd.Eline = par("lwd"), lty.Eline = par("lty"), col.Conf = "red", 
            lwd.Conf = par("lwd"), lty.Conf = 2, cex.Cover = 0.7, 
            cex.legend = 0.8)

Arguments

Distr object of class "UnivariateDistribution": distribution of the summands
n vector of integers: sample sizes to be considered
m integer: (total) number of replicates to be plotted subsequently
step integer: number of replicates to be drawn at once
sleep numeric: pause in seconds between subsequent plots
withEline logical: shall a line for the limiting expectation (in case of class Cauchy instead: median) be drawn?
withConf logical: shall (CLT-based) confidence bands be plotted?
withCover logical: shall empirical coverage of (CLT-based) confidence bands be printed?
withLegend logical: shall a legend be included?
CLTorCheb character: type of confidence interval —"CLT" or "Chebyshev"; partial matching is used; if this fails "CLT" is used.
coverage numerical: nominal coverage of the confidence bands —to be in (0,1)
col.Eline character or integer code; color for confidence bands
lwd.Eline integer code (see par); line width of the confidence bands
lty.Eline integer code (see par); line type of the confidence bands
col.Conf character or integer code; color for confidence bands
lwd.Conf integer code (see par); line width of the confidence bands
lty.Conf integer code (see par); line type of the confidence bands
cex.Cover magnification w.r.t. the current setting of cex to be used for empirical coverages; as in par
cex.legend magnification w.r.t. the current setting of cex to be used for the legend as in par
... further arguments to be passed to matplot, matlines, abline

Details

illustrateLLN generates a sequence of plots. Any parameters of plot.default may be passed on to this particular plot method.

There are default main titles as well as xlab and ylab annotations.

In all title arguments, the following patterns are substituted:

If not explicitly set, col.Eline, col.Conf are set to col if this arg is given and else to their default values as given above. Similarly for cex, lwd and lty.

Value

void

Author(s)

Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de

Examples

illustrateLLN(Distr = Unif())
illustrateLLN(Distr = Pois(lambda = 2))
illustrateLLN(Distr = Pois(lambda = 2)+Unif())
illustrateLLN(Td(3), m = 50, col.Eline = "green", lwd = 2, cex = 0.6, main = 
 "My LLN %C%Q", sub = "generated %D")
illustrateLLN(Td(3), m = 50, CLTorCheb = "Chebyshev") 
illustrateLLN(Td(3), m = 50, CLTorCheb = "Chebyshev", coverage = 0.75) 

[Package distrTeach version 2.0.4 Index]