Statistical inference of $P(X

Statistical inference of $P(X<Y)$ for the Burr Type XII distribution based on records

In this paper, the maximum likelihood and Bayesian approaches have been used to obtain the estimates of the stress-strength reliability $R=P(X<Y)$ based on upper record values for the two-parameter Burr Type XII distribution. A necessary and sufficient condition is studied for the existence and uniqueness of the maximum likelihood estimates of the parameters. When the first shape parameter of $X$ and $Y$ is commonand unknown, the maximum likelihood (ML) estimate and asymptotic confidence interval of $R$ are obtained. In this case, the Bayes estimateof $R$ has been developed by using Lindley's approximation and the Markov Chain Monte Carlo (MCMC) method due to lack of explicit forms under the squared error (SE) and linear-exponential (LINEX) loss functions for informative prior. The MCMC method has been also used to construct the highest posterior density (HPD) credible interval. When the first shape parameter of X and Y is common and known, the ML, uniformly minimum variance unbiased (UMVU) and Bayes estimates, Bayesian and HPD credible as well as exact and approximate intervals of $R$ are obtained. The comparison of the derived estimates is carried out by using Monte Carlo simulations. Two real life data sets are analysed for the illustration purposes.

Keywords:

Burr Type XII distribution, Stres-strength model Record values, Bayes estimation,

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Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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