see_the_clt_for_uniform: Illustration of the central limit theorem for sampling from...

In ipsRdbs: Introduction to Probability, Statistics and R for Data-Based Sciences

Illustration of the central limit theorem for sampling from the uniform distribution

Description

Illustration of the central limit theorem for sampling from the uniform distribution

Usage

see_the_clt_for_uniform(nsize = 10, nrep = 10000)

Arguments

nsize	Sample size, n. Its default value is 10.
nrep	Number of replications. How many samples of size nsize should be taken, default value is 10000.

Value

A vector of means of the replicated samples. The function also has the side effect of drawing a histogram of the sample means and two superimposed density functions: one estimated from the data using the density function and the other is the density of the CLT approximated normal distribution. The better the CLT approximation, the closer are the two superimposed densities.

Examples

a <- see_the_clt_for_uniform()
old.par <- par(no.readonly = TRUE) 
par(mfrow=c(2, 3))
a1 <- see_the_clt_for_uniform(nsize=1)
a2 <- see_the_clt_for_uniform(nsize=2)
a3 <- see_the_clt_for_uniform(nsize=5)
a4 <- see_the_clt_for_uniform(nsize=10)
a5 <- see_the_clt_for_uniform(nsize=20)
a6 <- see_the_clt_for_uniform(nsize=50)
par(old.par)
ybars <- see_the_clt_for_uniform(nsize=12)
zbars <- (ybars - mean(ybars))/sd(ybars)
k <- 100
u <- seq(from=min(zbars), to= max(zbars), length=k)
ecdf <-  rep(NA, k)
for(i in 1:k) ecdf[i] <- length(zbars[zbars<u[i]])/length(zbars)
tcdf <- pnorm(u)
plot(u, tcdf, type="l", col="red", lwd=4, xlab="", ylab="cdf")
lines(u, ecdf, lty=2, col="darkgreen", lwd=4)
symb <- c("cdf of sample means", "cdf of N(0, 1)")
legend(x=-3.5, y=0.4, legend = symb, lty = c(2, 1), 
col = c("darkgreen","red"), bty="n")

ipsRdbs documentation built on May 29, 2024, 4:15 a.m.