R/a_qnorm.R

In Sielinski/vacuum: Tukey's Vacuum Cleaner

#' Returns the typical value from a unit-normal distribution
#' @description
#' Returns the typical value from a unit-normal distribution for the
#' \emph{i}th ordered observation in an \emph{n}-sized sample.
#'
#' This is a helper function for FUNOP, which uses the output of this
#' function as the denominator for its slope calculation.
#' @param
#' i Non-zero index of an array
#' @param
#' n Non-zero length of the array
#' @return
#' Quantile of \code{i} from a unit-normal distribution
#' @seealso [vacuum::funop()]
#' @references
#' Tukey, John W. "The Future of Data Analysis."
#' \emph{The Annals of Mathematical Statistics},
#' \emph{33}(1), 1962, pp 1-67. \emph{JSTOR},
#' \url{https://www.jstor.org/stable/2237638}.
#' @examples
#' a_qnorm(i = 25, n = 42)
#' a_qnorm(21.5, 42)
#' @export

a_qnorm <- function(i, n) {
  if (is.numeric(i) & is.numeric(n)) {
    stats::qnorm((3 * i - 1) / (3 * n + 1))
  } else {
    warning('arguments "i" and "n" must be numeric')
  }

}