lln.ani {animation} | R Documentation |
This function plots the sample mean as the sample size grows to check whether the sample mean approaches to the population mean.
lln.ani(FUN = rnorm, mu = 0, np = 30, pch = 20, col.poly = "bisque", col.mu = "gray", ...)
FUN |
a function to generate random numbers from a certain distribution: function(n, mu) |
mu |
population mean; passed to FUN |
np |
times for sampling from a distribution (not the sample size!); to examine the behaviour of the sample mean, we need more times of sampling to get a series of mean values |
pch |
symbols for points; see Details |
col.poly |
the color of the polygon to annotate the range of sample means |
col.mu |
the color of the horizontal line which denotes the population mean |
... |
other arguments passed to points |
np
points are plotted to denote the distribution of the sample mean; we will observe that the range of the sample mean just becomes smaller and smaller as the sample size increases and ultimately there will be an obvious trend that the sample mean converges to the population mean mu
.
The parameter nmax
in ani.options
means the maximum sample size.
None (invisible `NULL
').
The argument pch
will influence the speed of plotting, and for a very large sample size (say, 300), it is suggested that this argument be specified as '.
'.
Yihui Xie
George Casella and Roger L. Berger. Statistical Inference. Duxbury Press, 2th edition, 2001.
http://animation.yihui.name/prob:law_of_large_numbers
oopt = ani.options(interval = 0.01, nmax = 150) lln.ani(pch = ".") # chi-square distribution; population mean = df lln.ani(function(n, mu) rchisq(n, df = mu), mu = 5, cex = 0.6) ## Not run: # save the animation in HTML pages ani.options(ani.height = 480, ani.width = 600, outdir = getwd(), nmax = 100, interval = 0.1, title = "Demonstration of the Law of Large Numbers", description = "The sample mean approaches to the population mean as the sample size n grows.") ani.start() par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0)) lln.ani(cex = 0.6) ani.stop() ## End(Not run) ani.options(oopt)