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

KIZILASLAN F., NADAR M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.46, sa.4, ss.713-742, 2017 (SCI-Expanded, Scopus, TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.15672/hjms.201510214218
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.713-742
  • Anahtar Kelimeler: Burr Type XII distribution, Stres-strength model, Record values, Bayes estimation, GENERALIZED EXPONENTIAL-DISTRIBUTION, LESS-THAN X, BAYESIAN-ESTIMATION, KUMARASWAMYS DISTRIBUTION, VALUES, MODEL, PREDICTION, LIKELIHOOD
  • Marmara Üniversitesi Adresli: Evet

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.