R/InverseNormalProbability.R

In jungd/ImproveISCAM: Investigating Statistical Concepts, Applications, and Methods

#' Inverse normal Probability
#'
#' @param prob1 Calculates the normal quantile of a specified probability
#' @param mean mean = 0
#' @param sd sd = 1
#' @param direction above,below, outside, or between
#'
#' @return Inverse Normal Probability
#' @export
#'
#' @examples
#'InNorm(0.88, direction="above")
#'InNorm(0.43, direction="below")
#'InNorm(0.95, direction="outside")
#'InNorm(0.88, direction="between")

InNorm<-function (prob1, mean = 0, sd = 1, direction){
  Description = "InNorm(prob1, mean=0, sd=1, direction) \n This function calculates the normal quantile of a specified probability. \n Input the desired probability and the parameters of the normal distribution or use standard normal. \n Specify whether you want this area to be \"above\", \"below\", or \"outside\" or \"between\". \n"
  if (as.character(prob1) == "?")
    stop(Description)
  min = mean - 4 * sd
  max = mean + 4 * sd
  thisx = seq(min, max, 0.001)
  plot(thisx, dnorm(thisx, mean, sd), xlab = "X=variable",
       ylab = "density", type = "l")
  newtitle = paste("Normal (mean =", mean, ", SD = ", sd, ")")
  title(newtitle)
  abline(h = 0, col = "gray")
  if (direction == "below") {
    answer = signif(qnorm(prob1, mean, sd, TRUE), 4)
    thisrange = seq(min, answer, 0.001)
    polygon(c(thisrange, answer, 0), c(dnorm(thisrange, mean,
                                             sd), 0, 0), col = "blue")
    text((min + answer)/2, dnorm(answer, mean, sd)/2, labels = prob1,
         pos = 2, col = "blue")
    text(answer, 0, labels = paste("X<", answer), col = "red")
    cat("the observation with", prob1, "probability below is",
        answer, "\n")
  }
  else if (direction == "above") {
    answer = signif(qnorm(prob1, mean, sd, FALSE), 4)
    thisrange = seq(answer, max, 0.001)
    polygon(c(answer, thisrange, max), c(0, dnorm(thisrange,
                                                  mean, sd), 0), col = "pink")
    text((answer + max)/2, (dnorm(answer, mean, sd)/2), labels = prob1,
         pos = 4, col = "blue")
    text(answer, 0, labels = paste("X>", answer), col = "red")
    cat("The observation with", prob1, "probability above is",
        answer, "\n")
  }
  else if (direction == "between") {
    answer1 = signif(qnorm((1 - prob1)/2, mean, sd, TRUE),
                     4)
    answer2 = mean + (mean - answer1)
    thisrange = seq(answer1, answer2, 0.001)
    polygon(c(answer1, thisrange, answer2), c(0, dnorm(thisrange,
                                                       mean, sd), 0), col = "pink")
    text(mean, dnorm(mean, mean, sd)/2, labels = prob1, col = "blue")
    text(answer1, 0, labels = paste("X>", answer1), col = "red")
    text(answer2, 0, labels = paste("X<", answer2), co = "red")
    cat("There is", prob1, "probability between", answer1,
        "and", answer2, "\n")
  }
  else if (direction == "outside") {
    answer1 = signif(qnorm(prob1/2, mean, sd, TRUE), 4)
    answer2 = mean + (mean - answer1)
    thisrange1 = seq(min, answer1, 0.001)
    thisrange2 = seq(answer2, max, 0.001)
    polygon(c(min, thisrange1, answer1), c(0, dnorm(thisrange1,
                                                    mean, sd), 0), col = "pink")
    polygon(c(answer2, thisrange2, max), c(0, dnorm(thisrange2,
                                                    mean, sd), 0), col = "pink")
    text(answer1, dnorm(answer1, mean, sd)/2, labels = prob1/2,
         col = "blue", pos = 2)
    text(answer2, dnorm(answer2, mean, sd)/2, labels = prob1/2,
         col = "blue", pos = 4)
    text(answer1, 0, labels = paste("X<", answer1), col = "red")
    text(answer2, 0, labels = paste("X>", answer2), col = "red")
    cat("There is", prob1, "probability outside", answer1,
        "and", answer2, "\n")
  }
}