illustrateLLN

From distrEx v1.9 by Matthias Kohl

Functions for Illustrating the LLN

Functions for generating a sequence of plots of randomly generated replicates of $\bar X_n= \frac{1}{n} \sum_{i=1}^n X_i$ 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.

Keywords: methods, distribution, dynamic

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)

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 's coerced to character} "%Q"{parameters of x in form of a comma-separated list of 's coerced to character and in parenthesis --- unless empty; then ""} "%N"{parameters of x in form of a comma-separated list = coerced to character} "%A"{deparsed argument x} "%D"{time/date-string when the plot was generated} "%X"{the expression $\bar X_n=\sum_{i=1}^n X_i/n$}

Value

void

code

lty

concept

illustration
teaching
LLN

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)

Documentation reproduced from package distrEx, version 1.9, License: GPL (version 2 or later)

Community examples

Looks like there are no examples yet.