Exponential scale mixture of matrix variate Cauchy distribution

Authors:
Amadou Sarr and Arjun K. Gupta

Journal:
Proc. Amer. Math. Soc. **139** (2011), 1483-1494

MSC (2010):
Primary 62H10; Secondary 62H12

Published electronically:
September 2, 2010

MathSciNet review:
2748443

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Abstract: In this paper, we introduce a new subclass of matrix variate elliptically contoured distributions that are obtained as a scale mixture of matrix variate Cauchy distribution and exponential distribution. We investigate its properties, such as stochastic representation and characteristic function. Unlike Cauchy distribution, it is shown that the generating variate of the new distribution possesses finite moments. The distributions of the unbiased estimators of and are derived. Furthermore, an identity involving a special function with a matrix argument is also obtained.

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Additional Information

**Amadou Sarr**

Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada

Email:
asarr@math.mcmaster.ca

**Arjun K. Gupta**

Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403

Email:
gupta@bgsu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10568-3

Keywords:
Matrix variate Cauchy,
scale mixture distribution,
exponential distribution,
stochastic representation,
Whittaker’s function,
Meijer’s function.

Received by editor(s):
December 14, 2009

Received by editor(s) in revised form:
May 1, 2010

Published electronically:
September 2, 2010

Communicated by:
Edward C. Waymire

Article copyright:
© Copyright 2010
American Mathematical Society