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

Naelah Alghufily; Khalaf S. Sultan; Mahmoud M. M. Mansour; Nagwa M. Mohamed; Naelah Alghufily; Khalaf S. Sultan; Mahmoud M. M. Mansour; Nagwa M. Mohamed

doi:10.3934/math.2026580

AIMS Mathematics

2026, Volume 11, Issue 5: 14121-14140. doi: 10.3934/math.2026580

Previous Article Next Article

Research article

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

1.
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, P. O. Box 11884, Cairo, Egypt
3.
Department of Basic Science, Faculty of Engineering, The British University in Egypt, El Sherouk City, Cairo, Egypt
4.
Department of Mathematics and Computer Sceince, Faculty of Science, Suez University, P.O. Box 43221, Suez, Egypt

Received: 10 March 2026 Revised: 22 April 2026 Accepted: 07 May 2026 Published: 19 May 2026
MSC : 60E05, 62E10, 62F15, 62N05, 62P30

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.
- unit-interval distribution,
- reliability analysis,
- bathtub-shaped hazard rate,
- Bayesian estimation,
- Markov chain Monte Carlo (MCMC)
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

Related Papers:

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.

References

[1]	J. Mazucheli, A. F. B. Menezes, L. B. Fernandes, R. P. de Oliveira, M. E. Ghitany, The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates, J. Appl. Stat., 47 (2019), 954–974. http://dx.doi.org/10.1080/02664763.2019.1657813 doi: 10.1080/02664763.2019.1657813
[2]	L. Tierney, Markov chains for exploring posterior distributions, Ann. Statist., 22 (1994), 1701–1728. http://dx.doi.org/10.1214/aos/1176325750 doi: 10.1214/aos/1176325750
[3]	M. V. Aarset, How to identify a bathtub hazard rate, IEEE Trans. Reliab., R-36 (1987), 106–108. http://dx.doi.org/10.1109/TR.1987.5222310 doi: 10.1109/TR.1987.5222310
[4]	I. J. González-Hernández, L. C. Méndez-González, R. Granillo-Macías, J. L. Rodríguez-Muñoz, J. S. Pacheco-Cedeño, A new generalization of the uniform distribution: Properties and applications to lifetime data, Mathematics, 12 (2024), 2328. http://dx.doi.org/10.3390/math12152328 doi: 10.3390/math12152328
[5]	J. Mazucheli, A. F. B. Menezes, M. E. Ghitany, The unit-Weibull distribution and associated inference, J. Appl. Probab. Stat., 13 (2018), 1–22.
[6]	L. D. Ribeiro-Reis, The unit inverse Weibull distribution and its associated regression model, J. Econom. Stat., 3 (2023), 55–68. https://doi.org/10.47509/JES.2023.v03i01.04 doi: 10.47509/JES.2023.v03i01.04
[7]	R. Xing, The application of coefficient of variation estimation in reliability study of existing structure, In: 2018 2nd IEEE advanced information management, communicates, electronic and automation control conference (IMCEC), 2018, 2652–2657. https://doi.org/10.1109/IMCEC.2018.8469617
[8]	N. Kumar, A. Dixit, V. Vijay, Entropy measures and their applications: A comprehensive review, arXiv: 2503.15660, 2025. https://doi.org/10.48550/arXiv.2503.15660
[9]	B. C. Arnold, N. Balakrishnan, H. N. Nagaraja, A first course in order statistics, 2008. https://doi.org/10.1137/1.9780898719062
[10]	N. U. Nair, P. G. Sankaran, N. Balakrishnan, Reliability modeling and analysis in discrete time, Academic Press, 2018. https://doi.org/10.1016/C2014-0-01528-6
[11]	R. L. Burden, J. D. Faires, A. M. Burden, Numerical analysis, 10 Eds., Cengage Learning, 2015.
[12]	A. C. Cohen, Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples, Technometrics, 7 (1965), 579–588. http://dx.doi.org/10.1080/00401706.1965.10490300 doi: 10.1080/00401706.1965.10490300
[13]	H. R. Varian, A Bayesian approach to real estate assessment, In: Studies in Bayesian econometrics and statistics, North-Holland Pub. Co., 1975,195–208.
[14]	W. T. Shaw, I. R. C. Buckley, The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv: 0901.0434, 2009. https://arXiv.org/abs/0901.0434.
[15]	M. Ahsanullah, Handbook on univariate statistical distributions, Trafford, 2011.

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)