Approximation Operators, Exponential, q-Exponential, and Free Exponential Families

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dc.creatorBryc, Wlodzimierz
dc.creatorIsmail, Mourad
dc.date2005-12-11
dc.date.accessioned2026-07-07T08:07:25Z
dc.date.available2026-07-07T08:07:25Z
dc.descriptionUsing the technique developed in approximation theory, we construct examples of exponential families of infinitely divisible laws which can be viewed as deformations of the normal, gamma, and Poisson exponential families. Replacing the differential equation of approximation theory by a q-differential equation, we define the q-exponential families, and we identify all q-exponential families with quadratic variance functions when |q|<1. We elaborate on the case of q=0 which is related to free convolution of measures. We conclude by considering briefly the case q>1, and other related generalizations.
dc.identifierhttps://arxiv.org/abs/math/0512224
dc.identifierhttp://arxiv.org/abs/math/0512224
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130935
dc.subjectStatistics Theory
dc.subject62E10, 41A35, 44A10,33C45
dc.titleApproximation Operators, Exponential, q-Exponential, and Free Exponential Families
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