Objective Bayesian analysis based on upper record values from two-parameter Rayleigh distribution with partial information

Seo, Jung In; Kim, Yongku

doi:10.1080/02664763.2016.1251886

Cited by 9 publications

(14 citation statements)

References 16 publications

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“…(3.4) Seo and Kim (2017) proved that the posterior distribution (3.3) is proper by showing that the normalizing constant (3.4) is integrable for µ and σ. In the same way, we prove that the posterior distribution (3.1) is proper.…”

Section: Properties Of the Posterior Distributionmentioning

confidence: 99%

“…Remark 3. The reference prior (2.19) is the same as the reference prior with partial information provided in Seo and Kim (2017).…”

Section: Objective Priorsmentioning

confidence: 99%

“…By Remark 2, the resulting posterior is the same as that of Seo and Kim (2017). For comparison, we re-write the results with those based on the reference prior (2.19)…”

Section: Properties Of the Posterior Distributionmentioning

confidence: 99%

“…However, a Markov chain Monte Carlo (MCMC) technique should be applied to generate the MCMC samples from the marginal posterior distributions since marginal posterior distributions (3.5) and (3.6) cannot be reduced analytically to any well-known distribution. Seo and Kim (2017) considered the uniform distribution on (0, x U(1) ) as a proposed distribution in the Metropolis-Hastings algorithm and obtained satisfactory results. The Metropolis-Hastings algorithm is applied to generate MCMC samples µ i (i = 1, .…”

Section: Properties Of the Posterior Distributionmentioning

confidence: 99%

“…Soliman and Al-Aboud (2008) provided a subjective Bayesian inference method for the scale parameter and the reliability and failure rate functions based on the record values. Seo and Kim (2017) provided a noninformative prior with partial information to estimate unknown parameters and predict the future upper record values. This article focuses on inference based on the objective priors to avoid the risk from inappropriate prior information and reduce the effort in obtaining sufficient prior information.…”

Section: Introductionmentioning

confidence: 99%

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Objective Bayesian inference based on upper record values from Rayleigh distribution

Seo

Kim

2018

CSAM

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The Bayesian approach is a suitable alternative in constructing appropriate models for observed record values because the number of these values is small. This paper provides an objective Bayesian analysis method for upper record values arising from the Rayleigh distribution. For the objective Bayesian analysis, the Fisher information matrix for unknown parameters is derived in terms of the second derivative of the log-likelihood function by using Leibniz's rule; subsequently, objective priors are provided, resulting in proper posterior distributions. We examine if these priors are the PMPs. In a simulation study, inference results under the provided priors are compared through Monte Carlo simulations. Through real data analysis, we reveal a limitation of the appropriate confidence interval based on the maximum likelihood estimator for the scale parameter and evaluate the models under the provided priors.

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Section: Properties Of the Posterior Distributionmentioning

confidence: 99%

“…Remark 3. The reference prior (2.19) is the same as the reference prior with partial information provided in Seo and Kim (2017).…”

Section: Objective Priorsmentioning

confidence: 99%

“…By Remark 2, the resulting posterior is the same as that of Seo and Kim (2017). For comparison, we re-write the results with those based on the reference prior (2.19)…”

Section: Properties Of the Posterior Distributionmentioning

confidence: 99%

Section: Properties Of the Posterior Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations