Novel constructing adequate simultaneous predictive limits or confidence intervals for future outcomes via pivotal quantities and ancillary statistics in the case of parametric uncertainty of applied real-life models

Abstract

In this paper, we consider the problems of constructing simultaneous predictive limits on future outcomes of all of l future samples using the results of a previous sample from the same underlying distribution belonging to invariant family. The approach used here emphasizes pivotal quantities relevant for obtaining ancillary statistics and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. It does not require the construction of any tables and is applicable whether the data are complete or Type II censored. The lower simultaneous predictive limits are often used as warranty criteria by manufacturers. The technique used here emphasizes pivotal quantities relevant for obtaining ancillary statistics and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. Applications of the proposed procedures are given for the two-parameter exponential distribution. The proposed technique is based on a probability transformation and pivotal quantity averaging to solve real-life problems in all areas including engineering, science, industry, automation & robotics, business & finance, medicine and biomedicine. It is conceptually simple and easy to use. The exact lower simultaneous predictive limits are found and illustrated with a numerical example.