# ssmsn: Scale-Shape Mixtures of Skew-Normal Distributions In ssmsn: Scale-Shape Mixtures of Skew-Normal Distributions

## Description

It provides the density and random number generator.

## Usage

 1 2 dssmsn(x, mu= NULL,sigma2= NULL,lambda= NULL,nu= NULL,family="skew.t.t") rssmsn(n,mu= NULL,sigma2= NULL,lambda= NULL,nu= NULL,family="skew.t.t") 

## Arguments

 x vector of observations. n numbers of observations. mu location parameter. sigma2 scale parameter. lambda skewness parameter. nu degree freedom family distribution family to be used in fitting ("skew.t.t", "skew.generalized.laplace.normal, "skew.slash.normal")

## Details

As discussed in Jamalizadeh and Lin (2016) the scale-shape mixture of skew-normal (SSMSN) distribution admits the following conditioning-type stochasctic representation

Y=μ + σ τ_1^{-1/2}[Z_1 | (Z_2 < λ f^{-1/2} Z_1)],

where f = τ_1/τ_2 and (Z_1,Z_2) and (τ_1,τ_2) are independent. Alternatively the SSMSN distribution can be generated via the convolution-type stochastic representation, given by

Y=μ + σ ≤ft(\frac{τ_1^{-1/2} f^{1/2}}{√{f + λ^2}}Z_2 + \frac{λ τ_1^{-1/2}}{√{f + λ^2}}|Z_1|\right).

## Value

dssmsn gives the density, rssmsn generates a random sample.

The length of the result is determined by n for rssmsn, and is the maximum of the lengths of the numerical arguments for the other functions dssmsn.

## Author(s)

Rocio Maehara [email protected] and Luis Benites [email protected]

## References

Jamalizadeh, Ahad and Lin, Tsung-I (2016). A general class of scale-shape mixtures of skew-normal distributions: properties and estimation. Computational Statistics, 1-24.

## Examples

 1 2 3 4 5 6 7 rSTT <- rssmsn(n=1000,mu=-4,sigma2=1,lambda=1,nu=c(3,4),"skew.t.t");hist(rSTT) rSGLN <- rssmsn(n=1000,mu=-4,sigma2=1,lambda=1,nu=3,"skew.generalized.laplace.normal");hist(rSGLN) rSSN <- rssmsn(n=1000,mu=-4,sigma2=1,lambda=1,nu=3,"skew.slash.normal");hist(rSSN) dSTT <- dssmsn(0.5,mu=-4,sigma2=1,lambda=1,nu=c(3,4),"skew.t.t") dSGLN <- dssmsn(0.5,mu=-4,sigma2=1,lambda=1,nu=3,"skew.generalized.laplace.normal") dSSN <- dssmsn(0.5,mu=-4,sigma2=1,lambda=1,nu=3,"skew.slash.normal") 

ssmsn documentation built on May 30, 2017, 3:31 a.m.