R/shape_ecp.R

In ecpdist: Extended Chen-Poisson Lifetime Distribution

#### Bowley skewness and Moors kurtosis ####

#' Bowley skewness and Moors kurtosis
#'
#' @description
#' Computes robust skewness and kurtosis measures based on quantile function of
#' the extended Chen-Poisson (ecp) distribution.
#'
#' @param lambda,gamma  parameter values > 0.
#'
#' @param phi parameter value != 0.
#'
#' @param measure Specifies the type of measure to be computed. Possible
#' types are:
#'
#'  - 'bowley' for Bowley skewness,
#'  - 'moors' for Moors kurtosis.
#'
#' @return Numeric value of the Bowley skewness or the Moors kurtosis.
#'
#' @details
#' The Extended Chen-Poisson distribution has no closed-form expression
#' for the moments. Therefore, the classical measures of
#' skewness and kurtosis based on moments are intractable. In such cases,
#' quantile-based measures are often considered, namely the Bowley skewness and
#' Moors kurtosis.
#'
#' @examples
#' ecp_shape(2, 0.3, 30, measure = 'bowley') # Bowley skewness
#'
#' @export
#'
ecp_shape <- function(lambda, gamma, phi, measure) {

  # Check if arguments are numeric
  if (!all(sapply(list(lambda, gamma, phi), is.numeric))) {
    stop("non-numeric argument")
  }

  # Check for invalid arguments
  if (min(lambda <= 0) || min(gamma <= 0) ||
        phi == 0) {
    stop("Invalid arguments")
  }

  # Compute skewness or kurtosis measure
  q <- qecp(p = seq(1 / 8, 7 / 8, 1 / 8), lambda, gamma, phi)
  func <- switch(measure, bowley = (q[2] - 2 * q[4] + q[6]) / (q[6] - q[2]),
                 moors = (q[7] - q[5] - q[3] + q[1]) / (q[6] - q[2]),
                 stop("Invalid measure type. Use 'bowley' or 'moors'."))
  return(func)
}