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