The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications, and characterizations

Volume 13, Issue 1, pp 34--52
Publication Date: September 10, 2019 Submission Date: May 20, 2019 Revision Date: July 17, 2019 Accteptance Date: July 30, 2019


Haitham M. Yousof - Department of Statistics, Mathematics and Insurance, Benha University, Egypt. Mahdi Rasekhi - Department of Statistics, Malayer University, Malayer, Iran. Morad Alizadeh - Department of Statistics, Faculty of Sciences, Persian Gulf University, Bushehr, 75169, Iran. G. G. Hamedani - Department of Mathematics, Statistics and Computer Science, Marquette University, USA.


In this paper, we propose and study a new class of continuous distributions called the Marshall-Olkin exponentiated generalized G (MOEG-G) family which extends the Marshall-Olkin-G family introduced by Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, \(\bf 84\) (1997), 641--652]. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments are derived. Some characterizations for the new family are presented. Maximum likelihood estimation for the model parameters under uncensored and censored data is addressed in Section 5 as well as a simulation study to assess the performance of the estimators. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.