Pseudo-moment generating functions: Application to pseudo-Schur constant random vectors

Abstract

In this note we show that pseudo-analysis tools can be effective in obtaining results in a distorted probability framework. More precisely, we introduce the notion of pseudo-independence and that of pseudo-moment generating function, the latter representing a generalization of the pseudo-Laplace transform, and both aiming at extending the corresponding notions in the usual probabilistic context. We show that these concepts and their properties, and more in general pseudo-analysis, are particularly useful to provide characterization results for a class of bivariate random vectors that we call “pseudo-Schur constant” family which represents an extension of the Schur-constant class.