A unified parsimonious exponential-G family for modeling real-world data: theory and statistical inference

Eman M. Eldemery; Hisham M. Almongy; Khaled M. Mahfouz; Mohammed M. El Genidy; Ibrahim Elbatal; Hassan M. Aljohani; Ahmed Z. Afify; Eman M. Eldemery; Hisham M. Almongy; Khaled M. Mahfouz; Mohammed M. El Genidy; Ibrahim Elbatal; Hassan M. Aljohani; Ahmed Z. Afify

doi:10.3934/math.2026571

AIMS Mathematics

2026, Volume 11, Issue 5: 13865-13912. doi: 10.3934/math.2026571

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A unified parsimonious exponential-G family for modeling real-world data: theory and statistical inference

1.
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
4.
Department of Statistics, Mathematics, and Insurance, Benha University, Benha 13511, Egypt

Received: 03 March 2026 Revised: 22 April 2026 Accepted: 24 April 2026 Published: 18 May 2026
MSC : 60E05, 62F10, 62N05

This paper introduces a new parsimonious class of statistical models, called the flexible exponential-G (FEx-G) family. The primary motivation for proposing the FEx-G family lies in its structural simplicity and adaptability, as it accommodates any baseline distribution without introducing additional shape parameters, thereby avoiding unnecessary model complexity. Unlike many existing generator-based families, the FEx-G family is independent of previously established generators, making it a distinct and original contribution to distribution theory. Despite its parsimonious structure, the FEx-G family exhibits remarkable flexibility, being capable of modeling both monotone and nonmonotone failure rate functions, and therefore is suitable for analyzing a wide range of non-negative real-world data. A special case, termed the flexible exponential-Kumaraswamy (FExKw) distribution, is investigated in detail. The parameters of the FExKw model are estimated using nine different estimation methods, and extensive simulation studies are conducted to evaluate and rank their performance. The practical usefulness of the FExKw distribution is illustrated through applications to four real-life datasets from environmental science, industry, and medicine, where it demonstrates superior performance compared with several well-established competing distributions.
- Kumaraswamy distribution,
- T–X family,
- simulations,
- real data,
- maximum likelihood,
- mean residual life,
- failure rate
Citation: Eman M. Eldemery, Hisham M. Almongy, Khaled M. Mahfouz, Mohammed M. El Genidy, Ibrahim Elbatal, Hassan M. Aljohani, Ahmed Z. Afify. A unified parsimonious exponential-G family for modeling real-world data: theory and statistical inference[J]. AIMS Mathematics, 2026, 11(5): 13865-13912. doi: 10.3934/math.2026571

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Abstract

This paper introduces a new parsimonious class of statistical models, called the flexible exponential-G (FEx-G) family. The primary motivation for proposing the FEx-G family lies in its structural simplicity and adaptability, as it accommodates any baseline distribution without introducing additional shape parameters, thereby avoiding unnecessary model complexity. Unlike many existing generator-based families, the FEx-G family is independent of previously established generators, making it a distinct and original contribution to distribution theory. Despite its parsimonious structure, the FEx-G family exhibits remarkable flexibility, being capable of modeling both monotone and nonmonotone failure rate functions, and therefore is suitable for analyzing a wide range of non-negative real-world data. A special case, termed the flexible exponential-Kumaraswamy (FExKw) distribution, is investigated in detail. The parameters of the FExKw model are estimated using nine different estimation methods, and extensive simulation studies are conducted to evaluate and rank their performance. The practical usefulness of the FExKw distribution is illustrated through applications to four real-life datasets from environmental science, industry, and medicine, where it demonstrates superior performance compared with several well-established competing distributions.

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