Possibility transformation of the sum of two symmetric unimodal independent/comonotone random variables

Abstract

The paper extends author's previous works on a probability/possibility transformation based on a maximum specificity principle to the case of the sum of two identical unimodal symmetric random variables. This transformation requires the knowledge of the dependency relationship between the two added variables. In fact, the comonotone case is closely related to the Zadeh's extension principle. It often leads to the worst case in terms of specificity of the corresponding possibility distribution, but it may arise that the independent case is worse than the comonotone case, e.g. for symmetric Pareto probability distributions. When no knowledge about the dependence is available, a least specific possibility distribution can be obtained from Fréchet bounds.