Bayesian and E-Bayesian Estimation for a Modified Topp Leone–Chen Distribution Based on a Progressive Type-II Censoring Scheme

• Published in: Symmetry (Basel) 2024-08, Vol.16 (8), p.981
• Main Authors: Kalantan, Zakiah I., Swielum, Eman M., AL-Sayed, Neama T., EL-Helbawy, Abeer A., AL-Dayian, Gannat R., Abd Elaal, Mervat
• Format: Article
• Language: English
• Subjects: Algorithms; balanced linear exponential loss function; balanced squared error loss function; Bayesian analysis; Bayesian estimation; COVID-19; Datasets; E-Bayesian estimation; Engineering; Error analysis; Estimators; Markov chains; modified Topp–Leone–Chen distribution; Monte Carlo simulation; Mortality; Parameter estimation; Parameter modification; Programming languages; progressive censored samples; Skewed distributions
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym16080981

This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model.