The modified Muth distribution: Statistical properties, entropy measures, and parameter estimation

H. M. Barakat; H. S. Bakouch; Mohamed A. Abd Elgawad; Hatem Semary; M. A. Alawady; I. A. Husseiny; M. G. Enany; T. S. Taher; H. M. Barakat; H. S. Bakouch; Mohamed A. Abd Elgawad; Hatem Semary; M. A. Alawady; I. A. Husseiny; M. G. Enany; T. S. Taher

doi:10.3934/math.2026259

AIMS Mathematics

2026, Volume 11, Issue 3: 6269-6296. doi: 10.3934/math.2026259

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Research article Special Issues

The modified Muth distribution: Statistical properties, entropy measures, and parameter estimation

1.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
3.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
4.
Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
5.
Faculty of Computers and Information Systems, Egyptian Chinese University, Cairo 11528, Egypt

Received: 27 November 2025 Revised: 25 February 2026 Accepted: 03 March 2026 Published: 12 March 2026
MSC : 60B12, 62G30

In this study, the modified Muth distribution was introduced as a parsimonious lifetime model obtained by structurally modifying the Muth survival function. The proposed construction preserves the scale-family property while altering tail behavior and cumulative hazard growth. A statistical analysis was presented, including derivations of moments, the moment-generating function, and several entropy measures. Parameter estimation was carried out using maximum likelihood, and interval estimation was performed via the Fisher information matrix. The performance of the model was examined through extensive simulation studies and a real-world data application involving strength measurements of carbon fibers. In this application, the modified Muth distribution provides a competitive and, in several cases, improved fit compared with commonly used lifetime models.
- Muth distribution,
- exponential-type models,
- information measures,
- maximum likelihood estimation,
- reliability data
Citation: H. M. Barakat, H. S. Bakouch, Mohamed A. Abd Elgawad, Hatem Semary, M. A. Alawady, I. A. Husseiny, M. G. Enany, T. S. Taher. The modified Muth distribution: Statistical properties, entropy measures, and parameter estimation[J]. AIMS Mathematics, 2026, 11(3): 6269-6296. doi: 10.3934/math.2026259

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Abstract

In this study, the modified Muth distribution was introduced as a parsimonious lifetime model obtained by structurally modifying the Muth survival function. The proposed construction preserves the scale-family property while altering tail behavior and cumulative hazard growth. A statistical analysis was presented, including derivations of moments, the moment-generating function, and several entropy measures. Parameter estimation was carried out using maximum likelihood, and interval estimation was performed via the Fisher information matrix. The performance of the model was examined through extensive simulation studies and a real-world data application involving strength measurements of carbon fibers. In this application, the modified Muth distribution provides a competitive and, in several cases, improved fit compared with commonly used lifetime models.

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