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.