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#' @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)
}
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