Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics
A. M. Abd Al-Fattah
Statistics Department, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
R. E. Abd El-Kader
Statistics Department, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
A. A. El-Helbawy *
Statistics Department, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
G. R. Al-Dayian
Statistics Department, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the shape parameters, reliability and hazard rate functions of the exponentiated generalized inverted Kumaraswamy distribution are estimated using Bayesian approach. The Bayes estimators are derived under the squared error loss function and the linear-exponential loss function based on dual generalized order statistics. Credible intervals for the parameters, reliability and hazard rate functions are obtained. The Bayesian prediction (point and interval) for a future observation of the exponentiated generalized inverted Kumaraswamy distribution is obtained based on dual generalized order statistics. All results are specialized to lower record values and a numerical study is presented. Moreover, the theoretical results are applied on three real data sets.
Keywords: Exponentiated generalized distributions, Bayesian estimation, dual generalized order statistics, exponentiated generalized inverted Kumaraswamy distribution