Free Exponential Families as Kernel Families

Details Free Exponential Families as Kernel Families Free Exponential Families as Kernel Families

2006-01-12

arxiv.org/abs/math/0601273v4

Demonstr. Math., XLII (2009) 657-672

Mathematics

Probability

Major revision; same theorems in different layout. 12 pages

Scientific paper

Free exponential families have been previously introduced as a special case of the q-exponential family. We show that free exponential families arise also from a procedure analogous to the definition of exponential families by using the Cauchy-Stieltjes kernel instead of the exponential kernel. We use this approach to re-derive several known results and to study further similarities with exponential families and reproductive exponential models.

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