Bivariate Compound Exponentiated Survival Function of the Lomax Distribution: Estimation and Prediction
R. M. Refaey
Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
G. R. AL-Dayian
Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
A. A. EL-Helbawy *
Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
A. A. EL-Helbawy *
Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, bivariate compound exponentiated survival function of the Lomax distribution is constructed based on the technique considered by AL-Hussaini (2011). Some properties of the distribution are derived. Maximum likelihood estimation and prediction of the future observations are considered. Also, Bayesian estimation and prediction are studied under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a real data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.
Keywords: Lomax distribution, bivariate distributions, compound exponentiated survival functions, maximum likelihood estimators, prediction, Bayes estimators, Monte Carlo simulations