Communications in Statistics - Theory and Methods, ( ISI ), Volume (43), No (19), Year (2014-10) , Pages (4109-4122)

Title : ( Balakrishnan skew-t distribution and associated statistical characteristics )

Authors: Sobhan Shafiei , Mahdi Doostparast ,

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As a discussant of Arnold and Beaver (2002), Balakrishnan proposed a generalized skew-normal ($BSN$) distribution. This new model has been encountered in the literature for modeling various data sets. In this paper, we propose a new generalization of skew $t$-distribution of Azzalini and Capitanio (2003), denoted by $BST$, as a scale mixture of the $BSN$-distribution. This new model may be used for modeling data sets exhibiting a unimodal density function having some skewness as well as heavy tails with respect to the skew normal distribution. An explicit expression for the probability density function and a recurrence formula for the cumulative distribution function of the $BST$-distribution are derived. Some statistical characteristics of the proposed model including central moments, unimodality and stochastic orders are investigated. Two representation theorems for BST-distribution which may be used for generating copies from the new model are given. The problem of estimation of the unknown parameters on the basis of a random sample arising from $BST$-distribution are considered. For illustration proposes, a real data set on strength of glass fibres, due to Smith and Naylor (1987), is analyzed using the procedures obtained.

Keywords

Akaike's information criterion; Maximum likelihood estimation; Multivariate t distribution; Order statistics; Recurrence relation; Skewness; Stochastic
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@article{paperid:1028188,
author = {Sobhan Shafiei and Doostparast, Mahdi},
title = {Balakrishnan skew-t distribution and associated statistical characteristics},
journal = {Communications in Statistics - Theory and Methods},
year = {2014},
volume = {43},
number = {19},
month = {October},
issn = {0361-0926},
pages = {4109--4122},
numpages = {13},
keywords = {Akaike's information criterion; Maximum likelihood estimation; Multivariate t distribution; Order statistics; Recurrence relation; Skewness; Stochastic ordering},
}

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%0 Journal Article
%T Balakrishnan skew-t distribution and associated statistical characteristics
%A Sobhan Shafiei
%A Doostparast, Mahdi
%J Communications in Statistics - Theory and Methods
%@ 0361-0926
%D 2014

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