Estimation of P(Y X) for the L´evy distribution

Najarzadegan, Hosein; Babaii, Saman; Rezaei, Satar; Nadarajah, Saralees

doi:10.15672/hjms.2015599877

Cited by 8 publications

(6 citation statements)

References 34 publications

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“…substitute equation (14) in equation (3) we obtain the shrinkage reliability estimation of R (s,k) model as follows:…”

Section: The Shrinkage Weight Function (Sh1)mentioning

confidence: 99%

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On Shrinkage Estimation of R(s,k) Based on Exponentiated Weibull Distribution

2017

IJSR

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Abstract:In this paper, estimation of a reliability of the multi-component system in stress-strength model R (s,k) is considered, when the stress and strength are independent random variables and follows the Exponentiated Weibull Distribution (EWD) with known first shape parameter θ and, the second shape parameter α is unknown. Different shrinkage estimation methods of R (s,k) for (EWD) are introduced based on maximum likelihood and moment methods. The comparisons among the proposed estimators that depend on the simulation technique are made and mean squared error (MSE) is used as criteria.

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“…substitute equation (14) in equation (3) we obtain the shrinkage reliability estimation of R (s,k) model as follows:…”

Section: The Shrinkage Weight Function (Sh1)mentioning

confidence: 99%

“…Ghitany et al (2015), studied estimation of the reliability of stress-strength system from power Lindley distribution; [6]. Najarzadegan et al (2016), considered the estimation of P (Y<X) for the Levy distribution; [14].…”

Section: Introductionmentioning

confidence: 99%

On Shrinkage Estimation of R(s,k) Based on Exponentiated Weibull Distribution

2017

IJSR

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“…The estimation of the system reliability R = P (X < Y ) has been considered many times using both parametric and non-parametric methods [6,10,12,13,15,19,23,27]. Here, X and Y represent the stress and the strength, respectively.…”

Section: Introductionmentioning

confidence: 99%

Interval Estimation of the System Reliability for Weibull Distribution based on Ranked Set Sampling Data

Akgül¹,

Şenoğlu²,

Acıtaş³

2018

HJMS

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Inference for the system reliability R is one of the most popular problems in the areas of engineering, statistics, biostatistics and etc. Therefore, there exist considerable numbers of studies concerning this problem. Traditionally, simple random sampling (SRS) is used for estimating the system reliability. However, in recent years, ranked set sampling (RSS), cost effective and efficient alternative of SRS, is used to estimate the system reliability. In this study, we consider the interval estimation of R when both the stress and the strength are independent Weibull random variables based on RSS. We first obtain the asymptotic confidence interval (ACI) of R by using the maximum likelihood (ML) methodology. The bootstrap confidence interval (BCI) of R is also constructed as an alternative to ACI. An extensive Monte-Carlo simulation study is conducted to compare the performances of ACI and BCI of R for different settings. Finally, a real data set is analyzed to demonstrate the implementation of the proposed methods.

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“…The estimation of stress-strength model when X and Y are random variables having a specified distribution discussed by many authors starting from Birnbaum (1956), Basu (1964), Downtown (1973), Tong (1974Tong ( , 1977, Beg (1980), Iwase (1987), McCool (1991). Recently, Ali et al (2012), Greco and Ventura (2011), Rezaei et al (2010), Wong (2012), Shahsanaei and Daneshkhah (2013), Hussian (2013), Al-Mutairi et al (2013), Ghitany et al (2015), Najarzadegan et al (2016). The estimator of reliability parameter when X and Y are independent exponential random variables discussed by several authors such as Enis and Geisser (1971), Kelley et al (1976), Sathe and Shah (1981).…”

Section: Introductionmentioning

confidence: 99%

Maximum penalized likelihood estimation for a stress-strength reliability model using complete and incomplete data

Hassan

2018

CSAM

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The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.

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Estimation of P(Y X) for the L´evy distribution

Cited by 8 publications

References 34 publications

On Shrinkage Estimation of R(s,k) Based on Exponentiated Weibull Distribution

On Shrinkage Estimation of R(s,k) Based on Exponentiated Weibull Distribution

Interval Estimation of the System Reliability for Weibull Distribution based on Ranked Set Sampling Data

Maximum penalized likelihood estimation for a stress-strength reliability model using complete and incomplete data

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