Large sample prediction intervals for future geometric mean. A comparative study

This paper provides simulation comparisons among the perfor-mance of 11 possible prediction intervals for the geometric mean of a Pareto distribution with parameters (λ,β). Six different procedures were used to obtain these intervals, namely true inter-val, pivotal interval, maximum likelihood estimation interval, central limit theorem interval, variance stabilizing interval and a mixture of the above intervals. Some of these intervals are valid if the observed sample size n is large, others are valid if both, n and the future sample size m, are large. Some of these intervals require a knowledge of λ or β, while others do not. The simulation validation and efficiency study shows that intervals depending on the MLE's are the best. The second best intervals are those obtained through pivotal methods or variance stabilization transformations. The third group of intervalsis that which depends on the central limit theorem when A i s known. There are two intervals which proved to be unacceptable under any criterion.