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Generalized Quantification of Risk Associated with Extreme Events 1
Author(s) -
Mitsiopoulos James,
Haimes Yacov Y.
Publication year - 1989
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/j.1539-6924.1989.tb01244.x
Subject(s) - damages , sensitivity (control systems) , extreme value theory , function (biology) , probability density function , econometrics , mathematics , dimension (graph theory) , statistics , combinatorics , engineering , electronic engineering , evolutionary biology , political science , law , biology
In the partitioned multiobjective risk method (PMRM) the probability axis is typically partitioned into three regimes: high‐exceedance low‐consequence, intermediate‐exceedance intermediate‐consequence, and low‐exceedance high‐consequence (LE/HC). For each regime, the PMRM generates a conditional expected risk‐function given that the damage lies within the regime. The theme of this paper is the conditional expected‐risk function for the LE/HC regime. This function, denoted by f 4 (.), captures the behavior of the “extreme events” of an underlying decision‐making problem. The PMRM offers two advantages: (a) it isolates LE/HC events, allowing the decision‐maker(s) to focus on the impacts of catastrophies; and (b) it generates more valuable information than that obtained from the common unconditional expected‐risk function. Theoretical problems may arise from uncertainty about the behavior of the tail of the risk curve describing the underlying frequency of damages. When the number of physical observations in small (e.g., in flood frequency analysis), the analyst is forced to make assumptions about the density of damages. Each succeeding distributional assumption will generate a different value of f 4 (.). An added dimension of difficulty is also created by the sensitivity of f 4 (.) to the choice of the boundary of the LE/HC regime. This paper has two overall objectives: (a) to present distribution‐free results concerning the magnitude of f 4 (.); and (b) to use those results to obtain a distribution‐free estimate of the sensitivity of f 4 (.) to the choice of the boundary of the LE/HC regime. The above objectives are realized by extending, and further developing, existing inequalities for continuously distributed random variables.