scholarly journals Characterization of the Riesz exponential family on homogeneous cones

2019 ◽  
Vol 158 (1) ◽  
pp. 45-57 ◽  
Author(s):  
Hideyuki Ishi ◽  
Bartosz Kołodziejek
Keyword(s):  
Exponential Family ◽  
Homogeneous Cones

scholarly journals EXTENSION OF THE OLKIN AND RUBIN CHARACTERIZATION TO THE WISHART DISTRIBUTION ON HOMOGENEOUS CONES

2011 ◽  
Vol 14 (04) ◽  
pp. 591-611 ◽  
Author(s):  
I. BOUTOURIA ◽  
A. HASSAIRI ◽  
H. MASSAM
Keyword(s):  
Wishart Distribution ◽  
Symmetric Cone ◽  
Symmetric Matrices ◽  
Riesz Distribution ◽  
Homogeneous Cones ◽  
Homogeneous Cone

The Wishart distribution on a homogeneous cone is a generalization of the Riesz distribution on a symmetric cone which corresponds to a given graph. The paper extends to this distribution, the famous Olkin and Rubin characterization of the ordinary Wishart distribution on symmetric matrices.

A characterization of complex homogeneous cones

1980 ◽  
Vol 170 (2) ◽  
pp. 181-194 ◽  
Author(s):  
Alan T. Huckleberry ◽  
Eberhard Oeljeklaus
Keyword(s):  
Homogeneous Cones

scholarly journals A martingale characterization of Pólya-Lundberg processes

2006 ◽  
Vol 43 (03) ◽  
pp. 741-754 ◽  
Author(s):  
Birgit Niese
Keyword(s):  
Poisson Process ◽  
Exponential Family ◽  
Exponential Families ◽  
Counting Processes ◽  
Mixed Poisson Process ◽  
Martingale Characterization

We study exponential families within the class of counting processes and show that a mixed Poisson process belongs to an exponential family if and only if it is either a Poisson process or has a gamma structure distribution. This property can be expressed via exponential martingales.

scholarly journals A martingale characterization of Pólya-Lundberg processes

2006 ◽  
Vol 43 (3) ◽  
pp. 741-754 ◽  
Author(s):  
Birgit Niese
Keyword(s):  
Poisson Process ◽  
Exponential Family ◽  
Exponential Families ◽  
Counting Processes ◽  
Mixed Poisson Process ◽  
Martingale Characterization

We study exponential families within the class of counting processes and show that a mixed Poisson process belongs to an exponential family if and only if it is either a Poisson process or has a gamma structure distribution. This property can be expressed via exponential martingales.

scholarly journals Lévy processes time-changed by the first-exit time of the inverse Gaussian subordinator

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2545-2552
Author(s):  
Farouk Mselmi
Keyword(s):  
Lévy Processes ◽  
Exponential Family ◽  
Exit Time ◽  
Levy Processes ◽  
Variance Function ◽  
Inverse Gaussian ◽  
Natural Exponential Family ◽  
First Exit Time

This paper deals with a characterization of the first-exit time of the inverse Gaussian subordinator in terms of natural exponential family. This leads us to characterize, by means its variance function, the class of L?vy processes time-changed by the first-exit time of the inverse Gaussian subordinator.

scholarly journals SUFFICIENCY IN QUANTUM STATISTICAL INFERENCE: A SURVEY WITH EXAMPLES

2006 ◽  
Vol 09 (03) ◽  
pp. 331-351 ◽  
Author(s):  
ANNA JENČOVÁ ◽  
DÉNES PETZ
Keyword(s):  
Statistical Inference ◽  
Fisher Information ◽  
Exponential Family ◽  
Weyl Algebra ◽  
Quantum Fisher Information ◽  
Quantum Statistics ◽  
Quantum Statistical ◽  
Basic Concepts ◽  
Noncommutative Analogue

This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated in parallel to the measure theoretic case. It turns out that several classical examples and results have a noncommutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related to the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result.

A Characterization of One-Parameter Exponential Family of Distributions

1993 ◽  
Vol 43 (3-4) ◽  
pp. 253-256 ◽  
Author(s):  
P. N. Jani
Keyword(s):  
Power Series ◽  
Exponential Family ◽  
Exponential Family Of Distributions ◽  
Power Series Distributions ◽  
Family Of Distributions

A characterization through moments given by Khatri (1959) for power series distributions (p. s. d.) and by Ahsanullah (1992) for modified power series distributions (m.p.s.d.) bas been extended for the wider class viz one-parameter exponential family of distributions.

Sign in / Sign up

Export Citation Format

Share Document