10.57647/mathsci.2026.66781

A Novel Extension of the Marshall-Olkin Distribution: Reliability, Mathematical Properties, and Applications in Different Sciences

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  • Elham Moradi1,
  • Zahra Shokooh Ghazani*1,
  1. Department of Statistics and Mathematics, CT.C., Islamic Azad University, Tehran, Iran

Received: 2025-10-14

Revised: 2026-01-29

Accepted: 2026-02-10

Published in Issue 2026-03-31

Published Online: 2026-03-25

Copyright (c) 2026 Elham Moradi, Zahra Shokooh Ghazani (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Moradi, E., & Shokooh Ghazani, Z. (2026). A Novel Extension of the Marshall-Olkin Distribution: Reliability, Mathematical Properties, and Applications in Different Sciences. Mathematical Sciences, 20(1). https://doi.org/10.57647/mathsci.2026.66781
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Abstract

This paper introduces a new and flexible family of continuous probability distributions, referred to as the Exponentiated Chen Marshall–Olkin family. The linear representation of the proposed model is derived, and several of its statistical properties, including moments, quantile function, Rényi entropy, and reliability measures, are investigated. Parameter estimation for this family is discussed using the maximum likelihood method under both complete and right-censored samples, while three distance-based estimation approaches are also considered. A particular sub-model of this family, called the Exponentiated Chen Marshall-Olkin Weibull distribution, is also proposed and studied in detail. Its mathematical characteristics and related sub-models are explored, and four different estimation techniques-maximum likelihood, least squares, weighted least squares, and Anderson-Darling-are employed to estimate the unknown parameters. Furthermore, a comprehensive simulation study is conducted to assess the bias and mean square error of the estimators, followed by applications to real health and engineering datasets. The empirical results demonstrate that the Exponentiated Chen Marshall–Olkin family provides excellent flexibility for modeling data exhibiting skewness, heavy tails, reliability characteristics, and non-monotonic hazard rates, confirming its potential as a powerful tool in reliability and lifetime data analysis.

Keywords

  • Marshall-Olkin family of distributions,
  • Exponentiated-G family,
  • Chen-G family,
  • Generated Family,
  • Maximum Likelihood Estimation
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