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http://dx.doi.org/10.29220/CSAM.2018.25.4.411

Objective Bayesian inference based on upper record values from Rayleigh distribution  

Seo, Jung In (Department of Statistics, Daejeon University)
Kim, Yongku (Department of Statistics, Kyungpook National University)
Publication Information
Communications for Statistical Applications and Methods / v.25, no.4, 2018 , pp. 411-430 More about this Journal
Abstract
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.
Keywords
Bayesian analysis; Fisher information; objective priors; Rayleigh distribution; upper record values;
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