| clt.ani {animation} | R Documentation |
First of all, a number of obs observations are generated from a certain distribution for each variable X_j, j = 1, 2, ..., n, and n = 1, 2, ..., nmax, then the sample means are computed, and at last the density of these sample means is plotted as the sample size n increases, besides, the p-values from the normality test shapiro.test are computed for each n and plotted at the same time.
clt.ani(obs = 300, FUN = rexp, col = c("bisque", "red", "black"),
mat = matrix(1:2, 2), widths = rep(1, ncol(mat)),
heights = rep(1, nrow(mat)), ...)
obs |
the number of sample points to be generated from the distribution |
FUN |
the function to generate n random numbers from a certain distribution |
col |
a vector of length 2 specifying the colors of the histogram and the density line |
mat, widths, heights |
arguments passed to layout to set the layout of the two graphs. |
... |
other arguments passed to hist |
As long as the conditions of the Central Limit Theorem (CLT) are satisfied, the distribution of the sample mean will be approximate to the Normal distribution when the sample size n is large enough, no matter what is the original distribution. The largest sample size is defined by nmax in ani.options.
None.
Yihui Xie
E. L. Lehmann, Elements of Large-Sample Theory. Springer-Verlag, New York, 1999.
http://animation.yihui.name/prob:central_limit_theorem
clt.ani
dynamic, distribution, dplot
oopt = ani.options(interval = 0.1, nmax = 150)
op = par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3)
clt.ani(type = "s")
par(op)
## Not run:
# HTML animation page
ani.options(ani.height = 500, ani.width = 600, outdir = getwd(), nmax = 100,
interval = 0.1, title = "Demonstration of the Central Limit Theorem",
description = "This animation shows the distribution of the sample
mean as the sample size grows.")
ani.start()
par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3)
clt.ani(type = "h")
ani.stop()
## End(Not run)
ani.options(oopt)
# other distributions: Chi-square with df = 5
f = function(n) rchisq(n, 5)
clt.ani(FUN = f)
R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(animation)
> png(filename="images/clt.ani_%03d.png" ,width=480, height=480)
> ### Name: clt.ani
> ### Title: Demonstration of the Central Limit Theorem
> ### Aliases: clt.ani
> ### Keywords: dynamic distribution dplot
>
> ### ** Examples
>
>
> oopt = ani.options(interval = 0.1, nmax = 150)
> op = par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3)
> clt.ani(type = "s")
> par(op)
>
> ## Not run:
> ##D
> ##D # HTML animation page
> ##D ani.options(ani.height = 500, ani.width = 600, outdir = getwd(), nmax = 100,
> ##D interval = 0.1, title = "Demonstration of the Central Limit Theorem",
> ##D description = "This animation shows the distribution of the sample
> ##D mean as the sample size grows.")
> ##D ani.start()
> ##D par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3)
> ##D clt.ani(type = "h")
> ##D ani.stop()
> ## End(Not run)
> ani.options(oopt)
>
> # other distributions: Chi-square with df = 5
> f = function(n) rchisq(n, 5)
> clt.ani(FUN = f)
>
>
>
> dev.off()
null device
1
>
