10.57647/mathsci.2026.2002.11

Power Unit Haq Distribution: A Flexible Probability Model for Lifetime Data Analysis

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  • Mohammed Ahmed Alomair1,
  • Muhammad Ahsan-ul-Haq*2,
  1. Department of Quantitative Methods, School of Business, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
  2. College of Statistical Sciences, University of the Punjab, Lahore Pakistan

Received: 2025-11-16

Revised: 2026-01-07

Accepted: 2026-02-11

Published in Issue 2026-06-30

Published Online: 2026-04-17

Copyright (c) 2026 Mohammed Ahmed Alomair, Muhammad Ahsan-ul-Haq (Author)

Creative Commons License

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

How to Cite

Alomair, M. A., & Ahsan-ul-Haq, M. (2026). Power Unit Haq Distribution: A Flexible Probability Model for Lifetime Data Analysis. Mathematical Sciences, 20(2). https://doi.org/10.57647/mathsci.2026.2002.11
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Abstract

In this study, a new unit interval distribution defined on the unit interval is developed through a power transformation approach and termed the Power Unit Haq (PUH) distribution. Several key statistical properties of the new distribution are derived, including incomplete moments, moments, and associated measures, moment generating function, hazard function, mean residual life function, and Rényi entropy. The parameters of the proposed distribution are estimated using five estimation approaches, and their performance is evaluated through extensive Monte Carlo simulations. The flexibility and practical relevance of the new distribution are further demonstrated by utilizing three real datasets-one involving radiation, reactor pump failures, and kidney dialysis patients. The proposed distribution exhibits superior fitting performance compared to established competing unit interval distributions. Additionally, Bayesian estimation of the model parameter is carried out, enhancing the distribution’s applicability for real-world scenarios.

Keywords

  • Unit interval model,
  • Moments,
  • Reliability analysis,
  • Inference,
  • Lifetime data,
  • Bayesian analysis
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