Bayes estimation for the Pareto failure-model using Gibbs sampling

Tiwari, Ram C.; Yang, Yizhou; Zalkikar, Jyoti

doi:10.1109/24.537018

Cited by 19 publications

(8 citation statements)

References 8 publications

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“…Let r i denotes the numbers of failed systems due to component S i ={i},i=1,2,3,4,…n and, r 12 , r 13 ,…, r 1n, r 23 , r 24 ,…, r 2n ,& r 123,….n denote the number of failed systems when the cause is masked. Also let the masking probabilities as P(S i = {n}|T i = t i , K i = n) = P n ; P(S i = {1,2,3,4,…n}|T i = t i , K i = n) = 1-P n ; …etc.…”

Section: The Full Likelihood Functionmentioning

confidence: 99%

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Bayes approach for the series system with type-2 censoring

Meena¹,

Vasanthi²

2013

ijma

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This work is focusing on a series system with n statistically independent components, each of which has a Pareto distributed lifetime with parameters τ j and θ j , j=1,2,3,…,n and which are censored when the r-th sample fails. Many products have more than one cause of failure. In masked system life time data, the causes of exact failure are often unknown. These observations are referred as masked. It is assumed that the lifetime data of the series system are masked, and the masking probability is dependent. A Bayesian analysis via gibbs sampling is made for estimating the unknown parameters using likelihood function. The results obtained are validated by a numerical example.

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Section: The Full Likelihood Functionmentioning

confidence: 99%

“…Arnold & Press (1983) presented Bayesian estimation for the pareto reliability model, when the parameter τ was known and θ was unknown. When both were known, Tiwari et al (1996) developed a full Bayesian approach to estimate the parameters and reliability function using the Gibbs Sampler.…”

Section: Introductionmentioning

confidence: 99%

Bayes approach for the series system with type-2 censoring

Meena¹,

Vasanthi²

2013

ijma

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“…In a Bayesian point of view, many authors have studied statistical inferences on Pareto distribution (e.g., Press, 1983, 1989;Geisser, 1984Geisser, , 1985Lwin, 1972;Nigm and Hamdy, 1987;Tiwari, Yang and Zalkikar, 1996;Ko and Kim, 1999;Fernández, 2008;Kim et al, 2009;Kang, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…Although the family was originally applied to analyze socio-economic and natural phenomena with long tail, the family has potential for modeling reliability and lifetime data as well (Arnold and Press, 1983). The Pareto distribution has been used by many authors in a Bayesian viewpoint (e.g., Press, 1983, 1989;Geisser, 1984Geisser, , 1985Lwin, 1972;Nigm and Hamdy, 1987;Tiwari et al, 1996;Ko and Kim, 1999;Fernández, 2008;Kim et al, 2009;Kang, 2010). For the common scale parameter, Elfessi and Jin (1996) derived a class of improved estimators which uniformly dominates the MLE under a class of convex scale invariant loss functions.…”

Section: Introductionmentioning

confidence: 99%

Noninformative priors for common scale parameter in the regular Pareto distributions

Kang¹,

Kim²,

Kim

2012

Journal of the Korean Data and Information Science Society

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In this paper, we introduce the noninformative priors such as the matching priors and the reference priors for the common scale parameter in the Pareto distributions. It turns out that the posterior distribution under the reference priors is not proper, and Jeffreys' prior is not a matching prior. It is shown that the proposed first order prior matches the target coverage probabilities in a frequentist sense through simulation study.

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“…It has been found in describing distributions of studies of income, property values, insurance risk, stock prices fluctuations, migration, size of cities and firms, word frequencies, occurrences of natural resources, business failures, service time in queuing systems, error clustering in communications circuits and lifetime data, etc (Arnold and Press, 1983;Fernández, 2008). The Pareto distribution has been used by many authors in a Bayesian viewpoint (e.g., Press, 1983, 1989;Geisser, 1984Geisser, , 1985Lwin, 1972;Nigm and Hamdy, 1987;Tiwari et al, 1996;Ko and Kim, 1999;Fernández, 2008;Kim et al, 2009;. For the common scale parameter, Elfessi and Jin (1996) derived a class of improved estimators which uniformly dominates the MLE under a class of convex scale invariant loss functions.…”

Section: Introductionmentioning

confidence: 99%

Default Bayesian hypothesis testing for the scale parameters in nonregular Pareto distributions

Kang¹

2012

Journal of the Korean Data and Information Science Society

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This article deals with the problem of testing the equality of the scale parameters in nonregular Pareto distributions. We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and a real data example are provided.

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Bayes estimation for the Pareto failure-model using Gibbs sampling

Cited by 19 publications

References 8 publications

Bayes approach for the series system with type-2 censoring

Bayes approach for the series system with type-2 censoring

Noninformative priors for common scale parameter in the regular Pareto distributions

Default Bayesian hypothesis testing for the scale parameters in nonregular Pareto distributions

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