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.
Pseudo-moment generating functions: Application to pseudo-Schur constant random vectors / Mulinacci, Sabrina; Ricci, Massimo. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - ELETTRONICO. - 485:1 (June)(2024), pp. 108963.1-108963.13. [10.1016/j.fss.2024.108963]
Pseudo-moment generating functions: Application to pseudo-Schur constant random vectors
Mulinacci, Sabrina;Ricci, Massimo
2024
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.File | Dimensione | Formato | |
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