A new power G-family of distributions: Properties, estimation, and applications.

This article suggests a new method to expand a family of life distributions by adding a parameter to the family, increasing its flexibility. It is called the extended Modi-G family of distributions. We derived the general statistical properties of the proposed family. Different methods of estimation were presented to estimate the parameters for the proposed family, such as maximum likelihood, ordinary least square, weighted least square, Anderson Darling, right-tailed Anderson-Darling, Cramér-von Mises, and maximum product of spacing methods. A special sub-model with three parameters called extended Modi exponential distribution was derived along with different shapes of its density and hazard functions. Randomly generated data sets and different estimation methods were used to illustrate the behavior of parameters of the proposal sub-model. To illustrate the importance of the proposed family over the other well-known methods, applications to medicine and geology data sets were analyzed.
Competing Interests: The authors have declared that no competing interests exist.
(Copyright: © 2024 Gemeay et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)