On Cauchy-Stieltjes Kernel Families

Wlodek Bryc (1) , Raouf Fakhfakh (1) , Abdelhamid Hassairi (1)

1 Laboratory of Probability and Statistics

We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes family. We also investigate when the domain of means can be extended beyond the "natural domain".

Mots clés: exponential families; Cauchy kernel; free stable law

Domaines: Probabilités [math.PR]

Wlodek Bryc, Raouf Fakhfakh, Abdelhamid Hassairi. On Cauchy-Stieltjes Kernel Families. 2012. ⟨hal-00740301⟩