Probability distributions and their partitioning

Abstract

The partitioned multi‐objective risk method (PMRM) was developed for solving risk‐based multi‐objective decision making problems. Based on the premise that the expected value concept is not sufficient for proper decision making, the PMRM generates a number of conditional expected value functions (or risk functions) by partitioning the probability axis into probability ranges. The goal of partitioning the probability axis is to have better information on extreme events for decision making purposes. These conditional expectations are dependent on the chosen partitioning points. This paper analyzes how conditional expectations are sensitive to variations in partitioning. One of the risk functions is a measure of extreme and catastrophic events. By using the relationship between this particular risk function and the statistics of extremes, the sensitivity analysis is simplified. In many practical applications, it is difficult to determine which type of distribution function best represents the random process. Conditional expectations also depend on the choice of distribution, and the impact of this selection is discussed.