R/myChiSim.R

In josephhgrimes/MyPackage: For Applied Statistical Methods course

#' Chi-Square distribution function
#'
#' This function will create a histogram with annotation using the Chi-Square distribution. The histogram
#' will include a density plot and a theoretical curve.
#'
#' @param n1 integer representing sample size
#' @param sigma1 integer representing standard deviation
#' @param mean1 integer representing mean
#' @param iter integer representing number of iterations
#' @param ymax decimal or integer representing maximum y value
#' @param ... additional arguments
#'
#' @importFrom graphics hist
#' @importFrom graphics legend lines
#' @importFrom stats dchisq density rnorm sd var
#'
#' @export

myChiSim <- function(n1 = 10, sigma1 = 3, mean1 = 5, iter = 1000, ymax = 0.1, ...){    # adjust ymax to make graph fit
  x <- NULL
  y1 = rnorm(n1*iter, mean = mean1, sd = sigma1)# generate iter samples of size n1

  data1.mat = matrix(y1, nrow = n1, ncol = iter, byrow = TRUE) # Each column is a sample size n1

  ssq1 = apply(data1.mat, 2, var) # ssq1 is s squared

  w = (n1-1)*ssq1/sigma1^2      #chi-sq stat

  hist(w, freq = FALSE, ylim = c(0, ymax), # Histogram with annotation
       main = substitute(paste("Sample size = ",n[1]," = ", n1," statistic = ", chi^2)),
       xlab = expression(paste(chi^2, "Statistic",sep=" ")), las=1)
  lines(density(w), col = "Blue", lwd = 3) # add a density plot
  curve(dchisq(x,n1-1), add = TRUE,col = "Red", lty = 2, lwd = 3) # add a theoretical curve
  title = expression(chi^2 == frac((n[1]-1)*s^2, sigma^2)) #mathematical annotation -see ?plotmath
  legend(x = n1*1.2, y = ymax*.75, c("Simulated", "Theoretical"), col = c("Blue","Red"), lwd = 4, lty = 1:2, bty = "n", title = title) # Legend #
  return(list(w = w, summary = summary(w), sd = sd(w), fun ="Chi-sq")) # some output to use if needed
}