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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 39, Fasc. 6,
pages 337 - 360
DOI: 10.19195/0208-4147.39.2.6
 

WISHART LAWS AND VARIANCE FUNCTION ON HOMOGENEOUS CONES

Piotr Graczyk
Hideyuki Ishi
Bartosz Kołodziejek

Abstract: We present a systematic study of Riesz measures and their natural exponential families of Wishart laws on a homogeneous cone. We compute explicitly the inverse of the mean map and the variance function of a Wishart exponential family.

2000 AMS Mathematics Subject Classification: Primary: 15B48; Secondary: 62H05.

Keywords and phrases: Natural exponential families, variance function, Wishart laws, Riesz measure, homogeneous cones, graphical cones.

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