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

Kızılaslan, Fatih; Nadar, Mustafa

doi:10.15672/hjms.201510214218

Cited by 5 publications

(4 citation statements)

References 44 publications

(70 reference statements)

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“…Kotz et al [7] present a great review for the development of the stress-strength reliability. Some recent contributions about the statistical inferences of reliability can be found the following papers Tavirdizade and Gharehchobogh [8], Basirat et al [9], Kızılaslan and Nadar [10], Rasethuntsa and Nadar [11] and Çetinkaya and Genç [12].…”

Section: Formentioning

confidence: 99%

“…We obtain the joint posterior density of and given data as follows (10) where is the normalizing constant. Then, under the squared error loss (SEL) function, the Bayes estimate of , , is given by (11) Since the integral in Equation (11) cannot be obtained explicitly, we use the MCMC method to obtain the point estimate and HPD credible interval of .…”

Section: Bayesian Inference Ofmentioning

confidence: 99%

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Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records

Kızılaslan

2019

International Journal of Advances in Engineering and Pure Sciences

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In this paper, we consider the stress-strength reliability for record data when the distribution of random stress and strength have the type I extreme-value distribution. First, classical inference methods, namely uniformly minimum variance unbiased estimate (UMVUE) and maximum likelihood estimate (MLE), are used for. Second, Bayesian inference of are considered for gamma priors assumption. When the common parameter of stress and strength variables is known, the exact Bayes estimate and Bayesian credible interval of are obtained. Markov Chain Monte Carlo (MCMC) method are used to derive the Bayes estimate and highest probability density (HPD) credible interval of when the common parameter is unknown. Finally, Monte Carlo simulations are performed to compare the performance of the obtained estimates. A real data set about the weather temperature is analyzed to illustrate the performances of the derived estimators in the paper.

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Section: Formentioning

confidence: 99%

Section: Bayesian Inference Ofmentioning

confidence: 99%

Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records

Kızılaslan

2019

International Journal of Advances in Engineering and Pure Sciences

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“…Asgharzadeh et al [3] extended the results of [10] and considered the estimation of R based on the two-parameter generalized exponential records. Kızılaslan and Nadar [23] studied about the estimation of R based on upper records for Burr Type XII distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation of $Pr(X<Y)$ for exponential power records

Tanış

Saraçoğlu

Asgharzadeh

et al. 2023

Hacettepe Journal of Mathematics and Statistics

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In this study, we tackle the problem of estimation of stress-strength reliability R = Pr(X < Y) based on upper record values for Exponential Power distribution. We use the maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used to compute the Bayes estimation of R since the Bayes estimator can not be obtained analytically. We also derive asymptotic confidence interval based on the asymptotic distribution of the maximum likelihood estimator of R. We consider a Monte Carlo simulation study in order to compare the performances of the maximum likelihood estimators and Bayes estimators according to mean square error criteria. Finally, a real data application is presented.

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“…Ghitany et al (2015) developed inference procedures for the stress-strength parameter R based on the power Lindley model. Kizilaslan and Nadar (2017) studied the statistical inference of PðX < Y Þ for the Burr Type XII distribution based on records. Chen and Cheng (2017) considered the stress-strength reliability model for the exponentiated Pareto distributions.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis for stress–strength model from inverted exponentiated Rayleigh based on the hybrid censored sample

Panahi

2022

IJQRM

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PurposeThe study based on the estimation of the stress–strength reliability parameter plays a vital role in showing system efficiency. In this paper, considering independent strength and stress random variables distributed as inverted exponentiated Rayleigh model, the author have developed estimation procedures for the stress–strength reliability parameter R = P(X>Y) under Type II hybrid censored samples.Design/methodology/approachThe maximum likelihood and Bayesian estimates of R based on Type II hybrid censored samples are evaluated. Because there is no closed form for the Bayes estimate, the author use the Metropolis–Hastings algorithm to obtain approximate Bayes estimate of the reliability parameter. Furthermore, the author construct the asymptotic confidence interval, bootstrap confidence interval and highest posterior density (HPD) credible interval for R. The Monte Carlo simulation study has been conducted to compare the performance of various proposed point and interval estimators. Finally, the validity of the stress–strength reliability model is demonstrated via a practical case.FindingsThe performance of various point and interval estimators is compared via the simulation study. Among all proposed estimators, Bayes estimators using MHG algorithm show minimum MSE for all considered censoring schemes. Furthermore, the real data analysis indicates that the splashing diameter decreases with the increase of MPa under different hybrid censored samples.Originality/valueThe frequentist and Bayesian methods are developed to estimate the associated parameters of the reliability model under the hybrid censored inverted exponentiated Rayleigh distribution. The application of the proposed stress–strength reliability model will help the reliability engineers and also other scientists to estimate the system reliability.

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

Cited by 5 publications

References 44 publications

Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records

Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records

Estimation of $Pr(X<Y)$ for exponential power records

Reliability analysis for stress–strength model from inverted exponentiated Rayleigh based on the hybrid censored sample

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