# IllustCLT: Functions for Illustrating the CLT In distrTeach: Extensions of Package 'distr' for Teaching Stochastics/Statistics in Secondary School

## Description

Functions for generating a sequence of plots of the density and cdf of the consecutive standardized and centered sums of iid r.v. distributed according to a prescribed discrete or absolutely continuous distribution compared to the standard normal — uses the generic function `plotCLT`.

## Usage

 ```1 2``` ```illustrateCLT(Distr, len, sleep = 0) illustrateCLT.tcl(Distr, k, Distrname) ```

## Arguments

 `Distr` object of class `"AbscontDistribution"`, `"LatticeDistribution"` or `"DiscreteDistribution"`: distribution of the summands `len` integer: up to which number of summands plots are generated `k` integer: number of summands for which a plot is to be generated `Distrname` character: name of the summand distribution to be used as title in the plot `sleep` numeric: pause in seconds between subsequent plots

## Details

`illustrateCLT` generates a sequence of plots, while `illustrateCLT.tcl` may be used with Tcl/Tk-widgets as in demo `illustCLT_tcl.R`.

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## Author(s)

Matthias Kohl [email protected]
Peter Ruckdeschel [email protected]

## References

Kohl, M., Ruckdeschel, P., (2014): General purpose convolution algorithm for distributions in S4-Classes by means of FFT. J. Statist. Softw. 59(4): 1-25.

`plotCLT`
 ```1 2 3 4 5 6 7``` ```distroptions("DefaultNrFFTGridPointsExponent" = 13) illustrateCLT(Distr = Unif(), len = 10) distroptions("DefaultNrFFTGridPointsExponent" = 12) illustrateCLT(Distr = Pois(lambda = 2), len = 10) distroptions("DefaultNrFFTGridPointsExponent" = 13) illustrateCLT(Distr = Pois(lambda = 2)+Unif(), len = 10) illustrateCLT.tcl(Distr = Unif(), k = 4, "Unif()") ```