Open AccessAlpha-Skew Generalized t Distribution
Author(s) -
Şükrü Acıtaş,
Birdal Şenoğlu,
Olçay Arslan
Publication year - 2015
Publication title -
revista colombiana de estadística/revista colombiana de estadistica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.256
H-Index - 16
eISSN - 2389-8976
pISSN - 0120-1751
DOI - 10.15446/rce.v38n2.51665
Subject(s) - kurtosis , skew , skew normal distribution , mathematics , skewness , distribution (mathematics) , noncentral chi squared distribution , generalized beta distribution , log cauchy distribution , normal distribution , half normal distribution , inverse chi squared distribution , maximum likelihood , ratio distribution , generalized normal distribution , statistics , cumulative distribution function , distribution fitting , probability density function , mathematical analysis , probability distribution , asymptotic distribution , computer science , telecommunications , estimator
The alpha-skew normal (ASN) distribution has been proposed recently in the literature by using standard normal distribution and a skewing approach. Although ASN distribution is able to model both skew and bimodal data, it is shortcoming when data has thinner or thicker tails than normal. Therefore, we propose an alpha-skew generalized t (ASGT) by using the generalized t (GT) distribution and a new skewing procedure. From this point of view, ASGT can be seen as an alternative skew version of GT distribution. However, ASGT differs from the previous skew versions of GT distribution since it is able to model bimodal data sest as well as it nests most commonly used density functions. In this paper, moments and maximum likelihood estimation of the parameters of ASGT distribution are given. Skewness and kurtosis measures are derived based on the first four noncentral moments. The cumulative distribution function (cdf) of ASGT distribution is also obtained. In the application part of the study, two real life problems taken from the literature are modeled by using ASGT distribution.