The inverse Pareto–Chen distribution with properties and applications to real-world data across multiple fields

Fatimah M. Alghamdi; Ekramy A. Hussein; Mohammed Alqawba; Hassan M. Aljohani; Ahmed Z. Afify; Fatimah M. Alghamdi; Ekramy A. Hussein; Mohammed Alqawba; Hassan M. Aljohani; Ahmed Z. Afify

doi:10.3934/math.2026955

AIMS Mathematics

2026, Volume 11, Issue 8: 23718-23774. doi: 10.3934/math.2026955

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Research article

The inverse Pareto–Chen distribution with properties and applications to real-world data across multiple fields

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Statistics, Faculty of Commerce, Al-Azhar University, Egypt
3.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
4.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
5.
Department of Statistics, Mathematics, and Insurance, Benha University, Benha 13511, Egypt

Received: 17 February 2026 Revised: 23 June 2026 Accepted: 10 July 2026 Published: 03 August 2026
MSC : 60E05, 62E10, 62F10, 62N05

In this article, we propose a flexible extension of the Chen model, termed the odd inverse Pareto–Chen (OIPC) distribution. The proposed distribution accommodates a wide range of failure rate shapes, including decreasing, increasing, J-shaped, reversed J-shaped, bathtub, and upside-down bathtub forms. In addition, its density function is capable of capturing right-skewed, left-skewed, symmetric, J-shaped, reversed J-shaped, and concave-down shapes. Its fundamental mathematical properties are thoroughly investigated. The parameters of the OIPC distribution are estimated using eight well-established estimation methods. An extensive simulation study is conducted to assess the performance of these estimators under both small and large sample sizes. The practical relevance of the proposed model is demonstrated through the analysis of four real-world datasets drawn from engineering and medical applications. The empirical findings highlight the remarkable flexibility of the OIPC distribution, which consistently outperforms several competing models, suggesting it as a promising alternative for modeling data in insurance and finance sectors.
- Chen distribution,
- actuarial measures,
- percentile estimators,
- insurance data,
- simulations
Citation: Fatimah M. Alghamdi, Ekramy A. Hussein, Mohammed Alqawba, Hassan M. Aljohani, Ahmed Z. Afify. The inverse Pareto–Chen distribution with properties and applications to real-world data across multiple fields[J]. AIMS Mathematics, 2026, 11(8): 23718-23774. doi: 10.3934/math.2026955

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Abstract

In this article, we propose a flexible extension of the Chen model, termed the odd inverse Pareto–Chen (OIPC) distribution. The proposed distribution accommodates a wide range of failure rate shapes, including decreasing, increasing, J-shaped, reversed J-shaped, bathtub, and upside-down bathtub forms. In addition, its density function is capable of capturing right-skewed, left-skewed, symmetric, J-shaped, reversed J-shaped, and concave-down shapes. Its fundamental mathematical properties are thoroughly investigated. The parameters of the OIPC distribution are estimated using eight well-established estimation methods. An extensive simulation study is conducted to assess the performance of these estimators under both small and large sample sizes. The practical relevance of the proposed model is demonstrated through the analysis of four real-world datasets drawn from engineering and medical applications. The empirical findings highlight the remarkable flexibility of the OIPC distribution, which consistently outperforms several competing models, suggesting it as a promising alternative for modeling data in insurance and finance sectors.

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