Objective Bayesian analysis using reparameterization for Type-II hybrid censored Rayleigh data

다국어 초록 (Multilingual Abstract)

In a Rayleigh distribution, a scale parameter is a crucial determinant of data variability, making its accurate estimation essential for enhancing the predictive performance of statistical models. However, under a hybrid censoring scheme, obtaining a corresponding marginal distribution function is notoriously complex and often inefficient. This complexity poses significant challenges in deriving an exact form of the expected Fisher information which is foundational for constructing a frequentist confidence interval and defining objective priors in a Bayesian framework. This study develops an objective Bayesian approach that effectively circumvents the computational complexities inherent in a Type-II hybrid censoring framework, thereby facilitating the estimation of the scale parameter in the Rayleigh distribution. A key aspect of our approach is the straightforward derivation of the Jeffreys prior through reparameterization. Using the derived Jeffreys prior, Bayes estimators of the scale parameter and their posterior risks are obtained under both squared error and general entropy loss functions. In addition to point estimation, interval estimation for the scale parameter is performed. For comparison, the results derived from a conjugate prior are provided together, and the validity and applicability of our approach are demonstrated through Monte Carlo simulations and analysis of COVID-19 mortality rates in Italy.

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