Bayesian Estimation and Prediction for Exponentiated Inverted Topp-Leone Distribution

Document Type : Original Article

Authors

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

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

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

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

Abstract

This paper focuses on Bayesian estimation for the shape parameters, reliability and hazard rate functions of the exponentiated inverted distribution. Bayesian estimation is performed under two different loss functions. 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 Type II censored sample. Credible intervals for the parameters, reliability and hazard rate functions are derived. The Bayesian two-sample prediction (point and interval) for a future observation from independent future sample from the same distribution, exponentiated inverted Topp-Leone distribution, is obtained based on Type II censored sample. Numerical illustration is proposed, and some interesting comparisons are presented to investigate the theoretical results through some measurements of accuracy. Moreover, the results are applied to real data set to ensure the theoretical results and to prove the applicability of the exponentiated inverted Topp-Leone distribution in real life.

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