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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