| Type: | Package |
| Title: | Scale-Shape Mixtures of Skew-Normal Distributions |
| Version: | 0.2.0 |
| Date: | 2017-01-31 |
| Author: | Rocio Maehara and Luis Benites |
| Maintainer: | Luis Benites <lbenitesanchez@gmail.com> |
| Imports: | MCMCpack |
| Description: | It provides the density and random number generator for the Scale-Shape Mixtures of Skew-Normal Distributions proposed by Jamalizadeh and Lin (2016) <doi:10.1007/s00180-016-0691-1>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Repository: | CRAN |
| NeedsCompilation: | no |
| Packaged: | 2017-01-31 13:14:11 UTC; rmaehara |
| Date/Publication: | 2017-02-01 08:34:50 |
Scale-Shape Mixtures of Skew-Normal Distributions
Description
It provides the density and random number generator.
Details
| Package: | ssmsn |
| Type: | Package |
| Version: | 0.2 |
| Date: | 2017-01-31 |
| License: | GPL (>=2) |
Author(s)
Rocio Maehara rmaeharaa@gmail.com and Luis Benites lbenitesanchez@gmail.com
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.
See Also
Examples
#See examples for the ssmsn function linked above.
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=\mu + \sigma \tau_1^{-1/2}[Z_1 | (Z_2 < \lambda f^{-1/2} Z_1)],
where f = \tau_1/\tau_2 and (Z_1,Z_2) and (\tau_1,\tau_2) are independent. Alternatively the SSMSN distribution can be generated via the convolution-type stochastic representation, given by
Y=\mu + \sigma \left(\frac{\tau_1^{-1/2} f^{1/2}}{\sqrt{f + \lambda^2}}Z_2 + \frac{\lambda \tau_1^{-1/2}}{\sqrt{f + \lambda^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 rmaeharaa@gmail.com and Luis Benites lbenitesanchez@gmail.com
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")