gnlMeanVar: Mean, Variance, Skewness and Kurtosis of the Generalised...

In sjp/NormalLaplace: The Normal Laplace Distribution

Description

Functions to calculate the mean, variance, skewness and kurtosis of a specified Generalised Normal Laplace distribution.

Usage

gnlMean(mu = 0, sigma = 1, alpha = 1, beta = 1, rho = 1,
        param = c(mu, sigma, alpha, beta, rho))
gnlVar(mu = 0, sigma = 1, alpha = 1, beta = 1, rho = 1,
         param = c(mu, sigma, alpha, beta, rho))
gnlSkew(mu = 0, sigma = 1, alpha = 1, beta = 1, rho = 1,
         param = c(mu, sigma, alpha, beta, rho))
gnlKurt(mu = 0, sigma = 1, alpha = 1, beta = 1, rho = 1,
         param = c(mu, sigma, alpha, beta, rho))

Arguments

mu	Location parameter mu, default is 0.
sigma	Scale parameter sigma, default is 1.
alpha	Tail parameter alpha, default is 1.
beta	Tail parameter beta, default is 1.
rho	Scale parameter rho, default is 1.
param	Specifying the parameters as a vector of the form c(mu, sigma, alpha, beta, rho).

Details

Users may either specify the values of the parameters individually or as a vector. If both forms are specified, then the values specified by the vector param will overwrite the other ones.

The mean function is

E(X) = rho(mu + 1/alpha - 1/beta)

The variance function is

Var(X) = rho(sigma^2 + 1/alpha^2 + 1/beta^2)

The skewness function is

skewness = (2(beta^3 - alpha^3)) / (rho^(1/2)*(sigma^2*alpha^2*beta^2 + alpha^2 + beta^2)^2

The kurtosis function is

kurtosis = (6(alpha^4 + beta^4)) / (rho(sigma^2*alpha^2*beta^2 + alpha^2 + beta^2)^2

Value

gnlMean gives the mean of the Generalised Normal Laplace, gnlVar the variance, gnlSkew the skewness and gnlKurt the kurtosis.

Author(s)

Simon Potter

References

William J. Reed. (2006) The Normal-Laplace Distribution and Its Relatives. In Advances in Distribution Theory, Order Statistics and Inference, pp. 61–74. Birkhäuser, Boston.

Examples

param <- c(10, 1, 5, 9, 2)
gnlMean(param = param)
gnlVar(param = param)
gnlSkew(param = param)
gnlKurt(param = param)

curve(dgnl(x, param = param), -10, 10)

sjp/NormalLaplace documentation built on May 30, 2019, 12:06 a.m.