Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions

In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, unimodal, or bathtub-shaped hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model.

Automated summary

In this paper, a flexible and general family of distributions called the modified generalized-G (MGG) family is proposed based on an original power-exponential transformation approach. The elegance and significance of this family lie in its ability to modify standard distributions by changing their functional forms without adding new parameters or by compounding two or adding one or two shape parameters. The distributions in the MGG family can have various hazard rate functions, making them suitable for fitting real data sets encountered in applied fields.