Open Access

ARTICLE

On the Genesis of the Marshall-Olkin Family of Distributions via the T-X Family Approach: Statistical Modeling

Yang Zhenwu¹, Zubair Ahmad^2,*, Zahra Almaspoor², Saima K. Khosa³

1 College of Management and Economics, Tianjin University, Tianjin, China
2 Department of Statistics, Yazd University, Yazd, Iran
3 Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan

* Corresponding Author: Zubair Ahmad. Email:

Computers, Materials & Continua 2021, 67(1), 753-760. https://doi.org/10.32604/cmc.2021.012393

Received 29 June 2020; Accepted 14 September 2020; Issue published 12 January 2021

Abstract

In the last couple of years, there Has been an increased interest among the statisticians to define new families of distributions by adding one or more additional parameter(s) to the baseline distribution. In this regard, a number of families have been introduced and studied. One such example is the Marshall-Olkin family of distributions that is one of the most prominent approaches used to generalize the existing distributions. Whenever, we see a new method, the natural questions come in to mind are (i) what are the genesis of the newly proposed method and (ii) how did the proposed method is obtained. No doubt, the Marshall-Olkin family is a very useful method and has attracted the researchers. But, unfortunately, the authors failed to provide the explanation about the genesis of the method that how this family of distributions is obtained. To address this issue, in this article, an attempt Has been made to provide a straight forward computation about the genesis of the Marshall-Olkin family that somehow completes its derivation. The genesis of the Marshall-Olkin family is based on the T-X family approach. Furthermore, we have showed that other extensions of the Marshall-Olkin family can also be obtained via the T-X family method. Finally, a real-life application form insurance science is presented to illustrate the newly proposed extension of the Marshall-Olkin family.

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Keywords

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