Bayesian and Non-Bayesian Estimation of Pr{Y<X} in Two Parameters Lomax Distribution

by Ashour,S.K.,Abd-Elfattah,A.M.and Mandouh,R.M.

Abstract: In this paper, the Bayesian and non Bayesian estimation problem of reliability R= P(Y<X) will be considered when X and Y are two independent but not identically distributed belonging to Lomax distribution with two unknown parameters. The maximum likelihood estimator (MLE) of the two unknown parameters of Lomax distribution and the asymptotic variance-covariance matrix of them will be obtained. The MLE of the reliability R will be presented. Also the sampling distribution of the maximum likelihood estimators will be obtained. Posterior function of R and Bayes estimator of R will be discussed. Finally, numerical examples are given to illustrate some of theoretical results.

Key Words: Reliability; Stress- Strength model; Maximum likelihood estimator; Bayes estimator; Lomax distribution, Pearson system

Authors:
Ashour, S.K., ashoursamir@hotmail.com
Abd Elfattah, a_afattah@hotmail.com
Mandouh, R.M., rshmndoh@hotmail.com

Editor: Meintanis,Simos G.,simosmei@econ.uoa.gr

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