A unified gamma-generated Weibull–Pareto distribution for heavy-tailed and skewed data with applications to medicine, engineering, and environment

Christophe Chesneau; Ibrahim Sadok; Christophe Chesneau; Ibrahim Sadok

doi:10.3934/math.2026952

AIMS Mathematics

2026, Volume 11, Issue 8: 23629-23662. doi: 10.3934/math.2026952

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A unified gamma-generated Weibull–Pareto distribution for heavy-tailed and skewed data with applications to medicine, engineering, and environment

Christophe Chesneau ^{1
,
,},
Ibrahim Sadok ^2,3

1.
Department of Mathematics, University of Caen Normandy, Caen, France
2.
Department of Mathematics and Computer Science, Faculty of Exact Sciences, University of Bechar, Algeria
3.
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P. O. Box 89, 22000, Sidi Bel-Abbès, Algeria

Received: 09 May 2026 Revised: 29 June 2026 Accepted: 20 July 2026 Published: 03 August 2026
MSC : 62E15, 62F10

The development of flexible parametric models that simultaneously capture heavy tails and skewness remains a central challenge in statistical science. This paper introduces the gamma-generated Weibull–Pareto (GGWP) distribution, a novel hierarchical distribution that integrates a Weibull baseline with a Pareto tail kernel within a parsimonious and identifiable framework. The GGWP distribution offers a unified solution to complex data features, combining theoretical depth with methodological completeness. We provide a thorough treatment of the model's key properties and develop a comprehensive suite of frequentist and Bayesian estimation methods, with asymptotic properties rigorously established and finite-sample performance assessed through extensive simulations. Three real-world applications in medicine, engineering, and environmental science demonstrate the practical superiority of the GGWP distribution over state-of-the-art competitors. The model's theoretical tractability, methodological versatility, and empirical performance establish it as a powerful and reliable tool for complex data modelling across disciplines. By unifying heavy-tailed behaviour and skewness within a single coherent framework, this work lays a foundation for future developments in flexible parametric modelling and offers a robust alternative to conventional lifetime distributions.
- heavy-tailed distribution,
- multimodality,
- Bayesian inference,
- entropy measures,
- stress-strength reliability,
- order statistics,
- minimum distance estimation,
- maximum product of spacings
Citation: Christophe Chesneau, Ibrahim Sadok. A unified gamma-generated Weibull–Pareto distribution for heavy-tailed and skewed data with applications to medicine, engineering, and environment[J]. AIMS Mathematics, 2026, 11(8): 23629-23662. doi: 10.3934/math.2026952

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Abstract

The development of flexible parametric models that simultaneously capture heavy tails and skewness remains a central challenge in statistical science. This paper introduces the gamma-generated Weibull–Pareto (GGWP) distribution, a novel hierarchical distribution that integrates a Weibull baseline with a Pareto tail kernel within a parsimonious and identifiable framework. The GGWP distribution offers a unified solution to complex data features, combining theoretical depth with methodological completeness. We provide a thorough treatment of the model's key properties and develop a comprehensive suite of frequentist and Bayesian estimation methods, with asymptotic properties rigorously established and finite-sample performance assessed through extensive simulations. Three real-world applications in medicine, engineering, and environmental science demonstrate the practical superiority of the GGWP distribution over state-of-the-art competitors. The model's theoretical tractability, methodological versatility, and empirical performance establish it as a powerful and reliable tool for complex data modelling across disciplines. By unifying heavy-tailed behaviour and skewness within a single coherent framework, this work lays a foundation for future developments in flexible parametric modelling and offers a robust alternative to conventional lifetime distributions.

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