Mean, Variance, Skewness and Kurtosis of the Normal Laplace Distribution.

Description

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

Usage

nlMean(mu = 0, sigma = 1, alpha = 1, beta = 1,
         param = c(mu, sigma, alpha, beta))
nlVar(mu = 0, sigma = 1, alpha = 1, beta = 1,
         param = c(mu, sigma, alpha, beta))
nlSkew(mu = 0, sigma = 1, alpha = 1, beta = 1,
         param = c(mu, sigma, alpha, beta))
nlKurt(mu = 0, sigma = 1, alpha = 1, beta = 1,
         param = c(mu, sigma, alpha, beta))

Arguments

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(Y) = mu + 1/alpha - 1/beta.

The variance function is

var(Y) = sigma^2 + 1/sigma^2 + 1/beta^2.

The skewness function is

skewness = [2/alpha^3 - 2/beta^3]/[sigma^2 + 1/alpha^2 + 1/beta^2]^3/2.

The kurtosis function is

kurtosis = [6/alpha^4 + 6/beta^4]/[sigma^2 + 1/alpha^2 + 1/beta^2]^2.

Value

nlMean gives the mean of the skew hyperbolic nlVar the variance, nlSkew the skewness, and nlKurt the kurtosis.

Author(s)

David Scott d.scott@auckland.ac.nz, Jason Shicong Fu

References

William J. Reed. (2006) The Normal-Laplace Distribution and Its Relatives. In Advances in Distribution Theory, Order Statistics and Inference, pp. 61–74. Birkh<c3><a4>user, Boston.

Examples

param <- c(10,1,5,9)
nlMean(param = param)
nlVar(param = param)
nlSkew(param = param)
nlKurt(param = param)


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

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(NormalLaplace)
Loading required package: DistributionUtils
Loading required package: RUnit
Loading required package: GeneralizedHyperbolic
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/NormalLaplace/nlMeanVar.Rd_%03d_medium.png", width=480, height=480)
> ### Name: NormalLaplaceMeanVar
> ### Title: Mean, Variance, Skewness and Kurtosis of the Normal Laplace
> ###   Distribution.
> ### Aliases: NormalLaplaceMeanVar nlMean nlVar nlSkew nlKurt
> ### Keywords: distribution
> 
> ### ** Examples
> 
> param <- c(10,1,5,9)
> nlMean(param = param)
[1] 10.08889
> nlVar(param = param)
[1] 1.052346
> nlSkew(param = param)
[1] 0.01227981
> nlKurt(param = param)
[1] 0.009494488
> 
> 
> curve(dnl(x, param = param), -10, 10)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>