Statistics and Its Interface

Volume 10 (2017)

Number 4

The generalized half-t distribution

Pages: 727 – 734

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n4.a14

Authors

Bulut Y. Murat (Department of Statistics, Eskişehir Osmangazi University, Eskişehir, Turkey)

Jamalizadeh Ahad (Department of Statistics, Shahid Bahonar University, Kerman, Iran)

Fatma Zehra Dogru (Department of Statistics, Giresun University, Giresun, Turkey)

Olcay Arslan (Department of Statistics, Ankara University, Ankara, Turkey)

Abstract

In this paper, we introduce a new distribution as a scale mixture of the generalized half normal (GHN) distribution proposed by [3] and the generalized gamma (GG) distribution. Since the half-t (HT) distribution given in [10] is a special case of the new distribution, we call the new distribution as “generalized half-t (GHT)” distribution. We derive the probability density function (pdf) of the GHT distribution and study some of its properties. We give maximum likelihood (ML) estimators for its parameters based on the Expectation-Maximization (EM) algorithm. We provide a small simulation study to show the performances of the ML estimators for GHT distribution. Also, we give a real data example to illustrate the modeling performance of the proposed distribution over the GHN and HT distributions.

Keywords

EM algorithm, GG, GHN, GHT, HT, ML

2010 Mathematics Subject Classification

Primary 60E05, 62E15. Secondary 62F10.

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