Weak Law of Large Numbers

WeakLawLargeNumbers.R

####################################################################
#  WLLN

samp.size <- 5

mu <- 10
sigma <- 3


histN <- 1000

xbar <- rnorm( histN, mean = mu, sd = sigma/sqrt(samp.size) )


hist( xbar,
      xlim = mu + sigma*c(-3,3), 
      xlab = "", 
      ylab = "", 
      main = "Weak Law of Large Numbers", 
      sub = "Sample size is n")

abline( v = mu, lty = 3)



WLLN <- function( samp.size = 3,
                  mu = 0,
                  sigma = 1,
                  histN = 1000){
    require(TeachingDemos)
    xbar <- rnorm( histN, mean = mu, sd = sigma/sqrt(samp.size) )
        hist(xbar, freq = FALSE, xlim = c(-3,3))
        lines(density(xbar))
        abline( v = mu, lty = 3)
        mtext(expression(mu), cex=2, at = mu, col="blue")
    hist.refresh <- function(...){
        samp.size <- slider(no = 1)
        mu <- slider(no = 2)
        sigma <- slider(no = 3)
        histN <- slider(no = 4)
        xr <- mu + sigma*c(-3,3)
        xbar <- rnorm( histN, mean = mu, sd = sigma/sqrt(samp.size) )
    
        hist( xbar, 
              freq = FALSE, 
              xlim = c(-3,3),
              main = "Weak Law of Large Numbers",
              xlab = expression(paste("Sampling Distribution of ", bar(italic(X))))
              )
        lines(density(xbar))
        abline( v = mu, lty = 3, lwd= 2, col = "blue")
        mtext(expression(mu), cex=2, at = mu, col="blue")
    }
    
    slider( hist.refresh, 
            c("Sample size n", "Population mean", "Population standard deviation",                      "Simulations for hist()"),
            c(1, -3, 0.1, 10), 
            c(1000, 3, 2, 5000),
            c(1, 0.1, 0.1, 1), 
            c(1, 0, 1, 1000), 
            title = "Weak LLN Demo")
}