A new extension of Odd Half-Cauchy Family of Distributions: properties and applications with regression modeling

Subrata Chakraburty; Morad Alizadeh; Laba Handique; Emrah Altun; G. G. Hamedani

doi:10.21307/stattrans-2021-039

A new extension of Odd Half-Cauchy Family of Distributions: properties and applications with regression modeling

Subrata Chakraburty Department of Statistics, Dibrugarh University, Dibrugarh-786004, India ORCID:https://orcid.org/0000-0002-6405-1486 , Morad Alizadeh Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, 75169, Iran ORCID:https://orcid.org/0000-0001-6638-2185 , Laba Handique Department of Mathematics and Statistics, Golaghat Commerce College, Dibrugarh University, India ORCID:https://orcid.org/0000-0001-9255-2918 , Emrah Altun Department of Mathematics, Bartin University, Bartin 74100, Turkey ORCID:https://orcid.org/0000-0001-5065-2523 , G. G. Hamedani Department of Mathematical and Statistical Sciences Marquette University, USA, USA ORCID:https://orcid.org/0000-0001-7976-1088 Statistics in Transition new series, vol. 22, 2021, 4, pages: 77-100 Published online: 8 December 2021 DOI 10.21307/stattrans-2021-039

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ABSTRACT

The paper proposes a new family of continuous distributions called the extended odd half Cauchy-G. It is based on the T-X construction of Alzaatreh et al. (2013) by considering half Cauchy distribution for T and the exponentiated G(x;ξ) as the distribution of X. Several particular cases are outlined and a number of important statistical characteristics of this family are investigated. Parameter estimation via several methods, including maximum likelihood, is discussed and followed up with simulation experiments aiming to asses their performances. Real life applications of modeling two data sets are presented to demonstrate the advantage of the proposed family of distributions over selected existing ones. Finally, a new regression model is proposed and its application in modeling data in the presence of covariates is presented.

KEYWORDS

T-X method; regression; simulation; estimation

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