The exp-$G$ family of probability distributions

TL;DR

This paper introduces the exp-$G$ family of distributions, a new method for adding a parameter to existing distributions, with comprehensive mathematical properties and practical applications demonstrated on fatigue life data.

Contribution

A novel method for extending distributions with an additional parameter, including detailed properties and applications to Weibull and beta distributions.

Findings

Distribution class includes the reference distribution as a special case

Mathematical properties such as entropy and divergence are derived

Successful application to fatigue life data

Abstract

In this paper we introduce a new method to add a parameter to a family of distributions. The additional parameter is completely studied and a full description of its behaviour in the distribution is given. We obtain several mathematical properties of the new class of distributions such as Kullback-Leibler divergence, Shannon entropy, moments, order statistics, estimation of the parameters and inference for large sample. Further, we showed that the new distribution have the reference distribution as special case, and that the usual inference procedures also hold in this case. Furthermore, we applied our method to yield three-parameter extensions of the Weibull and beta distributions. To motivate the use of our class of distributions, we present a successful application to fatigue life data.