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


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Kizilaslan F., Nadar M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.46, ss.713-742, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 46 Konu: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.15672/hjms.201510214218
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.713-742

Özet

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 common and unknown, the maximum likelihood (ML) estimate and asymptotic confidence interval of R are obtained. In this case, the Bayes estimate of 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.