2024/03/11 by A. Asgharzadeh, Asgharzadeh, Akbar, Éric Marchand +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #62C10 #62C20 #62F15 #62N01 #62N05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Spatial and Panel Data Analysis #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2403.06718
openalex publication_date 2024/03/11 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28
For exponentially distributed lifetimes, we consider the prediction of future order statistics based on having observed the first m order statistics. We focus on the previously less explored aspects of predicting: (i) an arbitrary pair of future order statistics such as the next and last ones, as well as (ii) the next N future order statistics. We provide explicit and exact Bayesian credible regions associated with Gamma priors, and constructed by identifying a region with a given credibility 1-λ under the Bayesian predictive density. For (ii), the HPD region is obtained, while a two-step algorithm is given for (i). The predictive distributions are represented as mixtures of bivariate Pareto distributions, as well as multivariate Pareto distributions. For the non-informative prior density choice, we demonstrate that a resulting Bayesian credible region has matching frequentist coverage probability, and that the resulting predictive density possesses the optimality properties of best invariance and minimaxity.