R/den.R

In PSDistr: Distributions Derived from Normal Distribution

#' @title Expnormal Distribution
#'
#' @description
#' Density, distribution function, quantile function and random generation
#' for the Expnormal distribution with parameters a1, b1, a2, b2 and c.
#'
#' @param x real argument
#' @param a1 position parameter
#' @param b1 positive scale parameter
#' @param a2 position parameter
#' @param b2 positive scale parameter
#' @param c semi-fraction parameter
#' @return The function returns the value of the probability density function for the Expnormal distribution.
#' @rdname den
#'
#' @details
#' Probability density function
#' see formula (2.1) in the article
#' Cumulative distribution function
#' see formula (2.3)
#' Quantile functon
#' see proposition (2.2)
#' Random number generator
#' see proposition (2.6)
#'
#' @author
#' Piotr Sulewski, \email{piotr.sulewski@upsl.edu.pl}, Pomeranian UNiwersity in Slupsk.
#'
#' @references
#' {Sulewski, P. (2022). \emph{New Members of The Johnson Family of Probability Distributions:Properties and Application,} Accepted: February 2022. REVSTAT-Statistical Journal.}
#'
#' @examples
#' den(1,1,2,2,2,1)
#' pen(1,1,2,2,2,1)
#' qen(0.5,1,2,2,2,1)
#' ren(10,1,2,2,2,1)
#'
#' @export


den <- function (x, a1, b1, a2, b2, c) {
  dnorm <- NULL
  if (b1 > 0 & b2 > 0)
  {

    return((exp((a1 - x) / b1) / b1 + exp((x - a2) / b2) / b2)*
             dnorm(c - exp((a1 - x) / b1) + exp((x - a2) / b2), 0, 1))
  }
  else
  {
    return("b1 > 0 and b2 > 0")
  }
}