Article ID Journal Published Year Pages File Type
389191 Fuzzy Sets and Systems 2015 13 Pages PDF
Abstract

We focus on the task of calculating conditional probabilities of the form Prob(U≤x|V≤y)Prob(U≤x|V≤y). We point out that in this case the relevant probabilities, Prob(U≤x)Prob(U≤x) and Prob(V≤y)Prob(V≤y), have the nature of a cumulative distribution. This enables us to use the Sklar theorem to directly calculate the required joint probability as a simple binary aggregation of these marginals using a copula. Here the choice of copula reflects the type of correlation between U and V  . We study in considerable detail the effects of using different copulas. We also show that this enables us to simply and directly calculate the probability that U=xU=x conditioned on the knowledge of the Prob(V≤y)Prob(V≤y). We use this result to aid in decision-making where we compare alternative's expected payoffs based on the conditioned probabilities.

Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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