### 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 μ and Σ are derived. Furthermore, an identity involving a special function with a matrix argument is also obtained.

Original language | English |
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Pages (from-to) | 1483-1494 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 139 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*139*(4), 1483-1494. https://doi.org/10.1090/S0002-9939-2010-10568-3

**Exponential scale mixture of matrix variate cauchy distribution.** / Sarr, Amadou; Gupta, Arjun K.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 139, no. 4, pp. 1483-1494. https://doi.org/10.1090/S0002-9939-2010-10568-3

}

TY - JOUR

T1 - Exponential scale mixture of matrix variate cauchy distribution

AU - Sarr, Amadou

AU - Gupta, Arjun K.

PY - 2011/4

Y1 - 2011/4

N2 - 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 μ and Σ are derived. Furthermore, an identity involving a special function with a matrix argument is also obtained.

AB - 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 μ and Σ are derived. Furthermore, an identity involving a special function with a matrix argument is also obtained.

UR - http://www.scopus.com/inward/record.url?scp=79951836844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951836844&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2010-10568-3

DO - 10.1090/S0002-9939-2010-10568-3

M3 - Article

VL - 139

SP - 1483

EP - 1494

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -