Building finite support possibility distributions from probability inequalities

This paper extends previous work on univariate possibility distributions from a probability distribution  family to the bivariate case. The transition to a higher dimension raises two main issues: the extension of unimodality is not unique, and dependence between variables arises. We limit this study to the case of finite support symmetric star unimodal probability distributions and make no assumptions about marginal laws and their dependences; only information about the joint distribution is considered. In the case of unimodal probability distributions with finite support, we highlight the key role of the uniform distribution, which, as in one dimension, dominates the other distributions. Examples of finite support bivariate probability distributions are presented.