Estimation of p(y&lt;x) in the burr case: a comparative study

Awad, Adnan M.; Gharraf, Mohamed K.

doi:10.1080/03610918608812514

Cited by 80 publications

(27 citation statements)

References 4 publications

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“…The Bayes' estimator given in (6) depends on α and β, and that in (7) depends on α, which are the parameters of the prior distribution of θ. The parameters α and β, could be estimated by means of empirical Bayes' procedure (see Lindley (1969) and Awad and Gharraf (1986)). Given the random sample x, the likelihood function of θ has an inverse gamma density with shape parameter (m − 1) and scale parameter T 2 .…”

Section: Estimationmentioning

confidence: 99%

Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

Dey¹,

Dey²,

Maiti³

2015

AJS

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This paper derives Bayes shrinkage estimator of Rayleigh parameter and its associated risk function based on conjugate prior under the assumption of general entropy loss function for progressive Type-II censored data. Risk function of maximum likelihood estimate, Bayes estimate and Bayes shrinkage estimate have also been derived and compared. An empirical Bayes estimate procedure has been suggested to include a guess value in case of the Bayes shrinkage estimation. Risk function of empirical Bayes estimate and empirical Bayes shrinkage estimate have also been derived and compared. In conclusion, an illustrative example is presented to assess how the Rayleigh distribution fits a real data set.

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Section: Estimationmentioning

confidence: 99%

Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

Dey¹,

Dey²,

Maiti³

2015

AJS

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“…In the literature the estimation of R in the case of Weibull or exponential distributions has been obtained under the assumption of known location parameters, see, [19]. Some of the recent work on the stress-strength model can be seen in [12], [13], [14] and [20] etc.…”

Section: Introductionmentioning

confidence: 99%

On the estimation of stress strength reliability parameter of inverted exponential distribution

Singh¹,

Singh²,

Yadav³

et al. 2015

IJSW

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This paper aims to estimate the stress-strength reliability parameter R = P (Y < X), when X and Y are independent inverted exponential random variable. We have also disscused some fundamental properties of the considered distribution. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. The Bayesian estimation of the reliability parameter has been also discussed under the assumption of independent gamma prior. Numerical integration technique is used for Bayesian computation. The proposed estimators are compared in terms of their mean squared errors through the simulation study. Two real data sets representing survival of head and neck cancer patients are fitted using the inverted exponential distribution and used to estimate the stress-strength parameters and reliability.

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“…The theoretical and practical results on the theory and applications of the stress-strength relationships in industrial and economic systems during the last decades are collected in Kotz et al [9]. Awad and Charraf [1] provided a simulation study which compared three estimators for = ( < ) when and are two independent but not identically distributed Burr random variables. These estimators are the minimum variance unbiased, maximum likelihood and Bayes.…”

Section: Introductionmentioning

confidence: 99%

Estimation of R=P[Y less than X] for Burr type XII distribution based on ranked set sampling

Hassan

Assar

Yahia

2014

International Journal of Basic and Applied Sciences

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Estimation of p(y<x) in the burr case: a comparative study

Cited by 80 publications

References 4 publications

Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

On the estimation of stress strength reliability parameter of inverted exponential distribution

Estimation of R=P[Y less than X] for Burr type XII distribution based on ranked set sampling

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