R/ksldist.R

In alanarnholt/PASWR2: Probability and Statistics with R, Second Edition

#' @title Simulated Lilliefors' Test of Normality Values
#' 
#' @description Function to visualize the sampling distribution of \eqn{D_n}{D[n]} (the Kolmogorov-Smirnov one sample statistic) for simple and composite hypotheses
#'  
#' @param n sample size
#' @param sims number of simulations to perform
#' @param alpha desired \eqn{\alpha} level
#' 
#' @author Alan T. Arnholt <arnholtat@@appstate.edu> 
#'  
#' @seealso \code{\link{ksdist}}
#' @export
#' 
#' @examples
#' ksldist(n = 10, sims = 1500, alpha = 0.05)
#' @keywords hplot
#######################################################################
ksldist <- function (n = 10, sims = 10000, alpha = 0.05)
{
  Dn <- c()
  DnL <- c()
  for (i in 1:sims){
    x <- rnorm(n)
    mu <- mean(x)
    sig <- sd(x)
    Dn[i] <- ks.test(x, pnorm)$statistic
    DnL[i] <- ks.test(x, pnorm, mean = mu, sd = sig)$statistic
  }
  ys <- range(density(DnL)$y)
  xs <- range(density(Dn)$x)
  cv <- quantile(Dn, 1 - alpha)
  cvp <- quantile(DnL, 1 - alpha)
  plot(density(Dn), col = "blue", lwd = 2, ylim = ys, xlim = xs, main = "", 
       xlab="", sub = paste("Simulated critical value =", round(cv, 3), 
       "(simple hypothesis) and ", round(cvp, 3), "(composite hypothesis)\n for n =", n, 
       "when the alpha value =", alpha))
  title(main = list(expression(paste("Simulated Sampling Distribution of " , D[n]))))
  lines(density(DnL), col = "red", lwd = 2, lty = 2)
  legend(x = "topright", legend = c("Simple Hypothesis", "Composite Hypothesis"), 
         col = c("blue", "red"), xjust = 0, text.col = c("black", "black"), 
         lty = c(1, 2), bg = "gray95", cex = 1, lwd = 2)
  box()
  abline(h = 0)
}