Seminario di Probabilità e Statistica Matematica Dipartimento di Matematica "Guido Castelnuovo" Sapienza Università di Roma Aula del Consiglio 16 novembre 2021, ore 14

Gérard Letac Institut de Mathématiques de Toulouse, Université Paul Sabatier

Title: Duality of exponential families and large deviations

Abstract: Two positive measures on the real line with exponential moments are duals if the derivatives of their log-Laplace transforms are inverse to each other. We link this property with real exponential families and large deviations. We compute the duals of many classical exponential families when they exist, like Tweedie, Morris, Mora families, and a family on the integers generated by the dilogarithm distribution. We extend the definition and the calculations to multivariate exponential families like Wishart and the simple quadratic families of Muriel Casalis. Details are in arXiv 2104.05510

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