Statistical properties and inference for a new bounded lifetime model with application

Authors

• Naelah Alghufily, Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaFollow
• Khalaf S. Sultan Prof., Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt
• Mahmoud MansourFollow
• Nagwa Mohamed, Suez University

Document Type

Article

Publication Date

Spring 5-19-2026

Abstract

A new two-parameter distribution on the unit interval (0,1) that is used to model bounded lifetime and reliability data is reported in this paper. The model is developed based on a transformation-based process and has the ability to support flexible shapes of hazard rates, including bathtub behavior. Basic properties like moments, entropy measures, and order statistics are obtained. The estimation of the parameter is formulated by the maximum likelihood and Bayesian estimation, and Bayesian inference is based on the Markov Chain Monte Carlo model. The performance of estimators is evaluated by simulation. The model is fitted to unit distributions of normalized failure-time data of 50 devices in an experiment of life-testing, showing competitive good-of-fit to existing unit distributions. The new framework is a dynamic instrument that can be used to analyze data on unit-interval lifetimes.

Recommended Citation

Naelah Alghufily, Khalaf S. Sultan, Mahmoud M. M. Mansour, Nagwa M. Mohamed. Statistical properties and inference for a new bounded lifetime model with application[J]. AIMS Mathematics, 2026, 11(5): 14121-14140. doi: 10.3934/math.2026580