First of all, a number of obs observations are generated from a
certain distribution for each variable \(X_j\), \(j = 1, 2, \cdots, n\), and \(n = 1, 2, \cdots, nmax\), then
the sample means are computed, and at last the density of these sample means
is plotted as the sample size \(n\) increases (the theoretical limiting
distribution is denoted by the dashed line), 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, mean = 1, sd = 1, col = c("bisque", "red", "blue",
"black"), mat = matrix(1:2, 2), widths = rep(1, ncol(mat)), heights = rep(1,
nrow(mat)), xlim, ...)the number of sample means to be generated from the distribution based on a given sample size \(n\); these sample mean values will be used to create the histogram
the function to generate n random numbers from a certain
distribution
the expectation and standard deviation of the population
distribution (they will be used to plot the density curve of the
theoretical Normal distribution with mean equal to mean and sd equal
to \(sd/\sqrt{n}\); if any of them is NA, the density curve will
be suppressed)
a vector of length 4 specifying the colors of the histogram, the density curve of the sample mean, the theoretical density cuve and P-values.
arguments passed to layout to set the
layout of the two graphs.
the x-axis limit for the histogram (it has a default value if not specified)
other arguments passed to plot.default to plot the
P-values
A data frame of P-values.
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.