Applications of the novel extended Rayleigh distribution in statistical quality, censored data with application for engineering materials

Laila A. Al-Essa; Muhammad Imran; Farrukh Jamal; Laila A. Al-Essa; Muhammad Imran; Farrukh Jamal

doi:10.3934/math.2026577

AIMS Mathematics

2026, Volume 11, Issue 5: 14025-17074. doi: 10.3934/math.2026577

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Research article

Applications of the novel extended Rayleigh distribution in statistical quality, censored data with application for engineering materials

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia; Laalessa@pnu.edu.sa
2.
Assistant Director (Statistics), Agriculture Department, Government of Punjab, Pakistan; imranshakoor84@yahoo.com
3.
Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia

Received: 11 February 2026 Revised: 23 April 2026 Accepted: 07 May 2026 Published: 18 May 2026
MSC : 60E05, 62E15, 62F15, 62N01, 62P30

We introduce an extended three-parameter Rayleigh distribution using the genesis of a truncated discrete Bell distribution. The expressions for the $ r $th moment, Réyni entropy, and quantile function are presented. Moreover, a group acceptance sampling plan for a truncated life test using the median as a quality parameter is presented. Two estimation methods (classical and Bayesian) are used to estimate parameters. The practical relevance of the proposed model is demonstrated using two real-life datasets related to engineering materials. Bias and efficiency of the estimators are assessed through simulation. Additionally, we present a censored data application using data centered on the survival rates of kidney patients ($ n = 76 $, censored $ = 23.7\% $, event $ = 76.3\% $). However, the Kaplan–Meier survival curve supports the proposed exponentiated Bell Rayleigh distribution.
- acceptance sampling,
- Bayes estimation,
- Bell distribution,
- censored data,
- maximum likelihood estimation,
- statistical quality control
Citation: Laila A. Al-Essa, Muhammad Imran, Farrukh Jamal. Applications of the novel extended Rayleigh distribution in statistical quality, censored data with application for engineering materials[J]. AIMS Mathematics, 2026, 11(5): 14025-17074. doi: 10.3934/math.2026577

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Abstract

We introduce an extended three-parameter Rayleigh distribution using the genesis of a truncated discrete Bell distribution. The expressions for the $ r $th moment, Réyni entropy, and quantile function are presented. Moreover, a group acceptance sampling plan for a truncated life test using the median as a quality parameter is presented. Two estimation methods (classical and Bayesian) are used to estimate parameters. The practical relevance of the proposed model is demonstrated using two real-life datasets related to engineering materials. Bias and efficiency of the estimators are assessed through simulation. Additionally, we present a censored data application using data centered on the survival rates of kidney patients ($ n = 76 $, censored $ = 23.7\% $, event $ = 76.3\% $). However, the Kaplan–Meier survival curve supports the proposed exponentiated Bell Rayleigh distribution.

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