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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

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Exponential scale mixture of matrix variate Cauchy distribution
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by Amadou Sarr and Arjun K. Gupta
Proc. Amer. Math. Soc. 139 (2011), 1483-1494
DOI: https://doi.org/10.1090/S0002-9939-2010-10568-3
Published electronically: September 2, 2010
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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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Bibliographic 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
  • 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
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1483-1494
  • MSC (2010): Primary 62H10; Secondary 62H12
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10568-3
  • MathSciNet review: 2748443