{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,24]],"date-time":"2024-08-24T20:40:07Z","timestamp":1724532007507},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,7]],"date-time":"2023-01-07T00:00:00Z","timestamp":1673049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Zayed University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"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, \u201cunimodal\u201d, or \u201cbathtub-shaped\u201c 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.<\/jats:p>","DOI":"10.3390\/axioms12010067","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T11:38:27Z","timestamp":1673264307000},"page":"67","source":"Crossref","is-referenced-by-count":4,"title":["Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-6700-2316","authenticated-orcid":false,"given":"Mustafa S.","family":"Shama","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, CFY, King Saud University, Riyadh 12373, Saudi Arabia"},{"name":"Department of Mathematics, Osim Higher Institute of Administrative Science, Osim 12961, Egypt"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-2488-5224","authenticated-orcid":false,"given":"Farid","family":"El Ktaibi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Zayed University, Abu Dhabi 144534, United Arab Emirates"}]},{"given":"Jamal N.","family":"Al Abbasi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Al-Nahrain University, Baghdad 64074, Iraq"}]},{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, LMNO, CNRS-Universit\u00e9 de Caen, Campus II, Science 3, 14032 Caen, France"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-6723-6785","authenticated-orcid":false,"given":"Ahmed Z.","family":"Afify","sequence":"additional","affiliation":[{"name":"Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1093\/biomet\/84.3.641","article-title":"A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families","volume":"84","author":"Marshall","year":"1997","journal-title":"Biometrika"},{"key":"ref_2","first-page":"71","article-title":"Recent developments in Marshall-Olkin distributions","volume":"2","author":"Gillariose","year":"2020","journal-title":"Contrib. 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