Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

   
 

 

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 $ \boldsymbol{\mu}$ and $ \boldsymbol{\Sigma}$ 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