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

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 [e-mail] and Luis Benites [e-mail]

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

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 2, 2019, 12:29 p.m.