Statistical Inference of Normal Distribution Based on Several Divergence Measures: A Comparative Study

Abstract

Statistical predictive analysis is a very useful tool for predicting future observations. Previous literature has addressed both Bayesian and non-Bayesian predictive distributions of future statistics based on past sufficient statistics. This study focused on evaluating Bayesian and Wald predictive-density functions of a future statistic V based on a past sufficient statistic W obtained from a normal distribution. Several divergence measures were used to assess the closeness of the predictive densities to the future density. The difference between these divergence measures was investigated, using a simulation study. A comparison between the two predictive densities was examined, based on the power of a test. The application of a real data set was used to illustrate the results in this article.