Statistical analysis for the truncated unit exponentiated Ailamujia distribution under progressive Type–Ⅱ censoring

Faten S. Alamri; Ahlam H. Tolba; Hana S. Jabarah; Ahmed R. El-Saeed; Ahmed T. Ramadan; Faten S. Alamri; Ahlam H. Tolba; Hana S. Jabarah; Ahmed R. El-Saeed; Ahmed T. Ramadan

doi:10.3934/math.2026589

AIMS Mathematics

2026, Volume 11, Issue 5: 14341-14373. doi: 10.3934/math.2026589

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Statistical analysis for the truncated unit exponentiated Ailamujia distribution under progressive Type–Ⅱ censoring

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia; Fsalamri@pnu.edu.sa
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt; dr_ahamdy156@mans.edu.eg, hanajbarah1@gmail.com
3.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; aesaleh@imamu.edu.sa
4.
Department of Mathematics, Faculty of Science, Galala University, Suez 43713, Egypt; Ahmed_Taha@Gu.edu.eg

Received: 17 February 2026 Revised: 26 April 2026 Accepted: 07 May 2026 Published: 20 May 2026
MSC : 62-XX

This study introduces and investigates the truncated unit exponentiated Ailamujia (TUEA) distribution within the framework of a progressive Type–Ⅱ censoring scheme. By incorporating truncation on the unit interval, the proposed model extends the unit exponentiated Ailamujia distribution, significantly enhancing its flexibility for modeling bounded lifetime data. We derive the fundamental mathematical properties of the TUEA model, including the probability density function, the cumulative distribution function, reliability measures, and hazard rate functions. Statistical inference for the model parameters is developed within both frequentist and Bayesian frameworks using progressive Type–Ⅱ censored data. The maximum likelihood estimates are computed through the Newton–Raphson iterative algorithm, whereas Bayesian inference is carried out under symmetric squared error and asymmetric LINEX loss functions. Point estimates and highest posterior density credible intervals are obtained via Markov chain Monte Carlo (MCMC) sampling procedures. In addition, a comprehensive Monte Carlo simulation study is conducted to investigate the finite sample performance of the new estimators in terms of bias, mean square error, and confidence interval coverage probability. In addition, the practical usefulness of the TUEA distribution is shown via an analysis of a real-life data sets, where the new model exhibits a better fit than competing models.
- truncated unit exponentiated Ailamujia distribution,
- progressive Type–Ⅱ censoring,
- maximum likelihood estimation,
- Bayesian inference
Citation: Faten S. Alamri, Ahlam H. Tolba, Hana S. Jabarah, Ahmed R. El-Saeed, Ahmed T. Ramadan. Statistical analysis for the truncated unit exponentiated Ailamujia distribution under progressive Type–Ⅱ censoring[J]. AIMS Mathematics, 2026, 11(5): 14341-14373. doi: 10.3934/math.2026589

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Abstract

This study introduces and investigates the truncated unit exponentiated Ailamujia (TUEA) distribution within the framework of a progressive Type–Ⅱ censoring scheme. By incorporating truncation on the unit interval, the proposed model extends the unit exponentiated Ailamujia distribution, significantly enhancing its flexibility for modeling bounded lifetime data. We derive the fundamental mathematical properties of the TUEA model, including the probability density function, the cumulative distribution function, reliability measures, and hazard rate functions. Statistical inference for the model parameters is developed within both frequentist and Bayesian frameworks using progressive Type–Ⅱ censored data. The maximum likelihood estimates are computed through the Newton–Raphson iterative algorithm, whereas Bayesian inference is carried out under symmetric squared error and asymmetric LINEX loss functions. Point estimates and highest posterior density credible intervals are obtained via Markov chain Monte Carlo (MCMC) sampling procedures. In addition, a comprehensive Monte Carlo simulation study is conducted to investigate the finite sample performance of the new estimators in terms of bias, mean square error, and confidence interval coverage probability. In addition, the practical usefulness of the TUEA distribution is shown via an analysis of a real-life data sets, where the new model exhibits a better fit than competing models.

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