Document Type
Article
Source of Publication
Axioms
Publication Date
1-1-2023
Abstract
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.
DOI Link
ISSN
Publisher
MDPI AG
Volume
12
Issue
1
Disciplines
Mathematics
Keywords
bathtub hazard rate, data analysis, distribution family, goodness-of-fit, maximum product of spacings, parameter estimation, uniform distribution
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Shama, Mustafa S.; El Ktaibi, Farid; Al Abbasi, Jamal N.; Chesneau, Christophe; and Afify, Ahmed Z., "Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions" (2023). All Works. 5654.
https://zuscholars.zu.ac.ae/works/5654
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Gold: This publication is openly available in an open access journal/series