Estimating Predictive Inference for Responses from the Generalized Rayleigh Model based on Complete Sample

Abstract

In this paper, the likelihood function given a complete sample from the two-parameter generalized Rayleigh model is derived. By making use of the Bayesian framework, the posterior density function, the predictive density for a single future response, a bivariate future response, and several future responses are derived. A comparison of the predictive variability of the maximum likelihood estimates and some of its neighborhood estimates are provided. The predictive means, standard deviations, 95% highest predictive density intervals, and the shape characteristics for a single future response are determined. A real data set is utilized to illustrate the predictive results.