Free exponential families as kernel families

• Autorzy: Bryc W.
• Języki publikacji: EN

Abstrakty

EN

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 the approach analogous to the definition of exponential families by using the Cauchy-Stieltjes kernel 1/(1 - Qx) instead of the exponential kernel exp(Qx). We use this approach to re-derive some known results and to study further similarities with exponential families and reproductive exponential models.

Słowa kluczowe

EN

dispersion models; free cumulants

PL

modele rozrzutu; półniezmienniki wolne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 3
• Strony: 657--672
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Bryc W.

• Department of Mathematical Sciences University of Cincinnati, PO Box 210025, Cincinnati, OH 45221-0025, USA,

Bibliografia

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