A Monte Carlo Method for Estimating Prediction Limit for the Arithmetic Mean of Lognormal Sample

Abstract

A Monte Carlo (MC) method is suggested for calculating an upper prediction limit for the mean of a future sample of small size N from a lognormal distribution. This is done by obtaining a Monte Carlo estimator of the limit utilizing the future sample generated from the Gibbs sampler. For the Gibbs sampler, a full conditional posterior predictive distribution of each observation in the future sample is derived. The MC method is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries. In an example, practical application of the method is described.