Estimation of Pr(X &lt; Y) Using Record Values in the One and Two Parameter Exponential Distributions

Baklizi, Ayman

doi:10.1080/03610920701501921

Cited by 62 publications

(23 citation statements)

References 9 publications

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“…In recent years there has been a growing interest in the study of inference problems associated with stress-strength model and record values. The estimation problem of R = P(Y < X) based on record values was firstly considered by Baklizi (2008) who estimated the reliability function based on URV for one and two parameters exponential distribution. Subsequent papers extended this work assuming various lifetime distributions for stress and strength random variables, for instance Baklizi (2012) estimated R based on URV for the Weibull distribution.…”

Section: Estimation Of P(ymentioning

confidence: 99%

Estimation of P(Y X) using record values from the generalized inverted exponential distribution

Hassan

Marwa

Nagy

2018

Pak.j.stat.oper.res.

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This article deals with the estimation of R = P(Y < X) when X and Y are distributed as two independent generalized inverted exponential with common scale parameter and different shape parameters. The maximum likelihood and Bayesian estimators of R are obtained on the basis of upper record values and upper record ranked set samples. The Bayesian estimator cannot be obtained in explicit form, and therefore it has been achieved using Lindley approximation. Simulation study is performed to compare the reliability estimators in each record sampling scheme with respect to biases and mean square errors.

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Section: Estimation Of P(ymentioning

confidence: 99%

Estimation of P(Y X) using record values from the generalized inverted exponential distribution

Hassan

Marwa

Nagy

2018

Pak.j.stat.oper.res.

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“…Assume x U(1) , x U(2) ,…, x U(n) is the first upper record values observed form Lomax(λ, α), and y U(1) , y U(2) ,…, y U(m) is the first upper record values observed form Lomax(λ, β). Based on these samples, we can estimate R. Recently works on interval estimation of R were discussed in Rezaeia, Tahmasbib, and Mahmoodi (2010), Baklizi (2008a;2008b), and Shoukri, Chaudhary, and AlHalees (2005). First, consider the MLE of R and its distributional properties.…”

Section: Estimation Of R If λ Is Knownmentioning

confidence: 99%

“…Kakade, Shirke, and Kundu (2008) studied the exponentiated Gumbel case. Baklizi (2008a;2008b) studied some inference problems of estimating R based on record values. Kundu and Raqab (2009) considered the estimation of R when X and Y are independent and both having three parameter Weibull distribution with common shape and location parameters, but different scale parameters.…”

Section: Review Of Literaturementioning

confidence: 99%

Bayesian estimation of P[Y < X] Based on Record Values from the Lomax Distribution and MCMC Technique

Mahmoud

EL‐Sagheer

Soliman

et al. 2016

J. Mod. App. Stat. Meth.

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Our interest is in estimating the stress-strength reliability R = P [Y < X], where X and Y follow the Lomax distribution with common scale parameter. We discuss the problem in the situation where the stress measurements and the strength measurements are both in terms of records. Firstly, we obtain the MLE of R in general case (the common scale parameter is unknown). The MLE of the three unknown parameters can be obtained by solving one non-linear equation. We provide a simple fixed point type algorithm to find the MLE. We propose percentile bootstrap confidence intervals of R. A Bayes point estimator of R, and the corresponding credible interval using the MCMC sampling technique have been proposed. Secondly, assuming the common scale parameter is known, the MLE of R is obtained. Using exact distributions of the MLEs of the two unknown parameters, we construct the exact confidence interval of R. In this case, Bayes estimators have been obtained using Lindley's approximations. Analysis of a simulated data set has been presented for illustrative purposes. Finally, the different proposed methods have been compared via Monte Carlo simulation study.

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“…Literature review reveals the importance of the estimation of Stress-strength reliability under various lifetime distributions. In this regard mention may be made to Kotz et al (2003), Baklizi (2008aBaklizi ( , 2008b, Eryilmaz (2008aEryilmaz ( , 2008bEryilmaz ( , 2010Eryilmaz ( , 2011, Krishnamoorthy et al (2007Krishnamoorthy et al ( , 2009Krishnamoorthy et al ( , 2010, Krishnamoorthy and Lin (2010), Kundu and Raqab (2009), Rezaei et al (2010). Recently, Rao (2012Rao ( , 2013) studied the estimation of reliability in a multicomponent stress-strength model.…”

Section: Introductionmentioning

confidence: 99%

Estimation of R3 = Pr(Y3 > max(Y1, Y2)) for Exponential Distribution

Kundu¹

2017

JAS

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This paper deals with the estimation of the reliability function R3 = Pr(Y3 > max (Y1, Y2)), when the random variables Y1, Y2 and Y3 are independent exponential with respective unknown location parameters µ1, µ2 and µ3. Here we have derived several estimators of R3 which includes uniformly minimum variance unbiased estimator (UMVUE), Bayes estimator (BE) and generalized Bayes estimator(GBE). Moreover, we have compared these estimators based on their risks under different loss functions.

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Estimation of Pr(X < Y) Using Record Values in the One and Two Parameter Exponential Distributions

Cited by 62 publications

References 9 publications

Estimation of P(Y X) using record values from the generalized inverted exponential distribution

Estimation of P(Y X) using record values from the generalized inverted exponential distribution

Bayesian estimation of P[Y < X] Based on Record Values from the Lomax Distribution and MCMC Technique

Estimation of<i> R</i><sub><i>3</i></sub> = Pr(<i>Y<sub>3</sub> </i>> max(<i>Y<sub>1</sub>, Y<sub>2</sub></i>)) for Exponential Distribution

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