Prediction Methods for Upper and Lower Record Values and Their Interrelationships

Abstract

Point and interval prediction methods for upper record values from some continuous distributions are adapted to respective statistical methods for lower record values from corresponding underlying distributions, namely from inverted distributions as their related counterparts. Interrelationships between corresponding point predictors for future upper and lower record values, these are maximum observed likelihood and maximum-product-of-spacings predictors, as well as corresponding prediction intervals for record values based on pivot statistics are shown. By this, known and new point predictors and prediction intervals for upper or lower record values from particular distributions can directly be transferred to analogous methods for lower or upper record values from the respective inverted distributions. The findings are exemplified for upper record values from an exponential and a Pareto distribution related to lower record values from an inverted exponential and a power function distribution.