IllustLLN: Functions for Illustrating the LLN

In distrTeach: Extensions of Package 'distr' for Teaching Stochastics/Statistics in Secondary School

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:

"%C"

class of argument x

"%P"

parameters of x in form of a comma-separated list of <value>'s coerced to character

"%Q"

parameters of x in form of a comma-separated list of <value>'s coerced to character and in parenthesis — unless empty; then ""

"%N"

parameters of x in form of a comma-separated list <name> = <value> coerced to character

"%A"

deparsed argument x

"%D"

time/date-string when the plot was generated

"%X"

the expression \code{bar(X)[n]==~~sum(X[i],i==1,n)/n}

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 [e-mail]

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) 

distrTeach documentation built on Nov. 13, 2022, 1:07 a.m.