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

Fatih KIZILASLAN; Mustafa NADAR

Makale detayları

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

Yazarlar:

Fatih KIZILASLAN | Mustafa NADAR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2017 Vol.46 Issue 4, pp.713-742

Belge Tipi:

Makale

Yayın Tarihi:

7/2017

Belge Dili:

İngilizce

Document ID (Org No.):

2000452227

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

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)R=P(X<Y)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 XXX and YYY is commonand unknown, the maximum likelihood (ML) estimate and asymptotic confidence interval of RRR are obtained. In this case, the Bayes estimateof RRR 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 RRR 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.

Makale detayları

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

Yazarlar: Fatih KIZILASLAN | Mustafa NADAR

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2017 Vol.46 Issue 4, pp.713-742

Belge Tipi: Makale

Yayın Tarihi: 7/2017

Belge Dili: İngilizce

Document ID (Org No.): 2000452227

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

Sayı

Yazarlar:

Fatih KIZILASLAN | Mustafa NADAR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2017 Vol.46 Issue 4, pp.713-742

Belge Tipi:

Makale

Yayın Tarihi:

7/2017

Belge Dili:

İngilizce

Document ID (Org No.):

2000452227

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X