Approximating catastrophic risk through statistics of extremes

This paper studies the approximation of the partitioned multiobjective risk method's (PMRM) extreme‐event risk function ƒ 4 . The analytic expression of the approximation for ƒ 4 is derived through the use of the statistics of extremes for cases where the underlying distribution is of an extreme‐value type I, II, or III, and it thus provides an effective theoretical tool for understanding the behavior of conditional expected values for a large class of distribution functions used in science and engineering. The results are confirmed for example problems of normal, Gumbel, Weibull, Pareto, lognormal, and uniform distributions.