Estimation of the Topp-Leone Alpha Power Weibull Distribution Based on Lower Record Values

Document Type : Original Article

Authors

1 Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt

2 Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt

Abstract

This article focuses on obtaining the maximum likelihood and Bayes estimators of the Topp-Leone alpha power Weibull distribution based on lower record values. The unknown parameters are estimated by applying the maximum likelihood approach based on lower record values. Also, the Bayesian method is utilized using gamma distribution as an informative prior to obtain the Bayes estimators for the parameters of the Topp-Leone alpha power Weibull distribution based on lower record values. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function based on lower record values. Finally, a numerical illustration is presented to demonstrate and evaluate the theoretical results where the numerical demonstration includes a simulation study and an application on real data set. The maximum likelihood estimates are evaluated using Monte Carlo Simulation via Mathematica 11 and the Bayes estimates are calculated by applying Markov Chain Monte Carlo through R programming language.

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Computational Journal of Mathematical and Statistical Sciences
Volume 3, Issue 1
April 2024
Pages 145-160

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