# R/nig.parameter.R In vlyubchich/lawstat: Tools for Biostatistics, Public Policy, and Law

#### Documented in nig.parameter

#' Generate Parameters for the Normal Inverse Gaussian (NIG) Distribution
#'
#' Produce four parameters, alpha (tail heavyness), beta (asymmetry),
#' delta (scale), and mu (location) from the four variables: mean, variance,
#' kurtosis, and skewness.
#'
#' @details The parameters are generated with three conditions:
#' 1) \eqn{3\times kurtosis > 5\times skewness^2};
#' 2) \eqn{skewness > 0}, and
#' 3) \eqn{variance > 0}.
#' See \insertCite{Atkinson_1982;textual}{lawstat},
#' \insertCite{BarndorffNielsen_Blaesild_1983;textual}{lawstat}, and
#' \insertCite{Noguchi_Gel_2010;textual}{lawstat}.
#'
#' @param mean mean of the NIG distribution.
#' @param variance variance of the NIG distribution.
#' @param kurtosis excess kurtosis of the NIG distribution.
#' @param skewness skewness of the NIG distribution.
#'
#'
#' @return A list with the following numeric components:
#' \item{alpha}{tail-heavyness parameter of the NIG distribution.}
#' \item{beta}{asymmetry parameter of the NIG distribution.}
#' \item{delta}{scale parameter of the NIG distribution.}
#' \item{mu}{location parameter of the NIG distribution.}
#'
#' @references
#' \insertAllCited{}
#'
#'
#' @keywords distribution
#'
#' @author Kimihiro Noguchi, Yulia R. Gel
#'
#' @export
#' @examples
#' library(fBasics)
#' test <- nig.parameter(0, 2, 5, 1)
#' random <- rnig(1000000, alpha = test$alpha, beta = test$beta,
#'                mu = test$mu, delta = test$delta)
#' mean(random)
#' var(random)
#' kurtosis(random)
#' skewness(random)
#'
nig.parameter <- function(mean = mean,
variance = variance,
kurtosis = kurtosis,
skewness = skewness)
{
### stop the code if the parameters do not satisfy the constraints. ###
if (3 * kurtosis <= 5 * skewness^2) {
stop("3*kurtosis - 5*skewness^2 must be greater than 0.")
}
if (skewness < 0) {
stop("skewness must be nonnegative.")
}
if (variance < 0) {
stop("variance must be greater than 0.")
}
### parameter calculations ###
alpha <-
sqrt(9 * (3 * kurtosis - 4 * skewness ^ 2) / (variance * (3 * kurtosis -
5 * skewness ^ 2) ^ 2))
beta <- sqrt(9 * skewness ^ 2 / (variance * (3 * kurtosis - 5 * skewness ^
2) ^ 2))
delta <-
3 * sqrt(variance * (3 * kurtosis - 5 * skewness ^ 2)) / (3 * kurtosis -
4 * skewness ^ 2)
mu <- mean - delta * beta / sqrt(alpha ^ 2 - beta ^ 2)
### display output ###
return(list(alpha = alpha, beta = beta, delta = delta, mu = mu))
}

vlyubchich/lawstat documentation built on April 17, 2023, 12:47 a.m.