Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution

• Published in: Revstat Vol. 23; no. 1; p. 117
• Main Authors: Agiwal, Varun, Tyagi, Shikhar, Chesneau, Christophe
• Format: Journal Article
• Language: English
• Published: Instituto Nacional de Estatistica 01.01.2025; Instituto Nacional de Estatística | Statistics Portugal
• Subjects: Analysis; Bayesian inference; Burr distribution; data analysis; Distribution (Probability theory); Information management; Maximum likelihood method; stress-strength reliability
• ISSN: 1645-6726; 2183-0371
• DOI: 10.57805/revstat.v23i1.544

* In this article, we propose and study a new three-parameter heavy-tailed distribution that unifies the Burr type XII and power inverted Topp-Leone distributions in an original manner. This unification is made through the use of a simple 'shift parameter'. Among its interesting functionalities, it exhibits possibly decreasing and unimodal probability density and hazard rate functions. We examine its quantile function, stochastic dominance, ordinary moments, weighted moments, incomplete moments, and stress-strength reliability coefficient. Then, the classical and Bayesian approaches are developed to estimate the model and stress-strength reliability parameters. Bayes estimates are obtained under the squared error and entropy loss functions. Simulated data are considered to point out the performance of the derived estimates based on the mean squared error. In the final part, the potential of the new model is exemplified by the analysis of two engineering data sets, showing that it is preferable to other reputable and comparable models. Keywords: * Burr distribution; Bayesian inference; maximum likelihood method; stress-strength reliability; data analysis. AMS Subject Classification: * 62E15, 60E05, 62F10.