A flexible power generated Topp–Leone distribution for modelling bounded lifetime data: Theory, simulation, and applications

Vidya Yerneni; Aafaq A. Rather; Sadiah M. Aljeddani; M. I. Khan; Alaa A. Elnazer; Vidya Yerneni; Aafaq A. Rather; Sadiah M. Aljeddani; M. I. Khan; Alaa A. Elnazer

doi:10.3934/math.2026949

AIMS Mathematics

2026, Volume 11, Issue 8: 23551-23587. doi: 10.3934/math.2026949

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Research article

A flexible power generated Topp–Leone distribution for modelling bounded lifetime data: Theory, simulation, and applications

1.
Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune, India
2.
Department of Mathematics, Al-Lith University College, Umm Al-Qura University, Al- Lith, 21961, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
4.
Department of Marketing, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

Received: 13 April 2026 Revised: 04 July 2026 Accepted: 24 July 2026 Published: 03 August 2026
MSC : 62A86, 62F12, 62G07

The increasing demand for flexible probabilistic models in medical survival analysis motivates the development of advanced extensions for bounded lifetime data. In this paper, we obtain a novel generalization of the Topp-Leone distribution using the power generalized Dinesh Uma Singh (PGDUS) transformation. The role of an additional shape parameter substantially enhances model flexibility, enabling it to capture diverse distributional shapes and various hazard rate behaviors, including monotonic and non-monotonic patterns, which has been discussed. Fundamental statistical properties of the proposed distribution are derived, including explicit expressions for the density and distribution functions, moments, quantile function, and key reliability measures. Parameter estimation is addressed through maximum likelihood and alternative methods, and their finite-sample performance is examined via Monte Carlo simulation. Measures of uncertainty and inequality, such as entropy and Bonferroni curves, are also investigated. The applicability and effectiveness of the proposed model are demonstrated using real medical survival dataset. Comparative results indicate better goodness-of-fit relative to some of the existing competing models. Overall, the PGDUS-generated Topp-Leone distribution provides a flexible framework for modelling bounded lifetime phenomena.
- PGDUS transformation,
- Topp-Leone distribution,
- maximum likelihood method,
- bounded distribution,
- reliability
Citation: Vidya Yerneni, Aafaq A. Rather, Sadiah M. Aljeddani, M. I. Khan, Alaa A. Elnazer. A flexible power generated Topp–Leone distribution for modelling bounded lifetime data: Theory, simulation, and applications[J]. AIMS Mathematics, 2026, 11(8): 23551-23587. doi: 10.3934/math.2026949

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Abstract

The increasing demand for flexible probabilistic models in medical survival analysis motivates the development of advanced extensions for bounded lifetime data. In this paper, we obtain a novel generalization of the Topp-Leone distribution using the power generalized Dinesh Uma Singh (PGDUS) transformation. The role of an additional shape parameter substantially enhances model flexibility, enabling it to capture diverse distributional shapes and various hazard rate behaviors, including monotonic and non-monotonic patterns, which has been discussed. Fundamental statistical properties of the proposed distribution are derived, including explicit expressions for the density and distribution functions, moments, quantile function, and key reliability measures. Parameter estimation is addressed through maximum likelihood and alternative methods, and their finite-sample performance is examined via Monte Carlo simulation. Measures of uncertainty and inequality, such as entropy and Bonferroni curves, are also investigated. The applicability and effectiveness of the proposed model are demonstrated using real medical survival dataset. Comparative results indicate better goodness-of-fit relative to some of the existing competing models. Overall, the PGDUS-generated Topp-Leone distribution provides a flexible framework for modelling bounded lifetime phenomena.

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