Abstract #300900

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JSM 2002 Abstract #300900
Activity Number: 102
Type: Topic Contributed
Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #300900
Title: On Multivariate Skew-normal Distributions
Author(s): John Chen*+ and Arjun Gupta
Affiliation(s): Bowling Green State University and Bowling Green State University
Address: MSC 428, Bowling Green, Ohio, 43403, USA
Keywords: Moment generating function ; Helmert matrix ; stochastic representation ; quadratic form ; multivariate normal distribution ; skew-normal distribution
Abstract:

According to the current definition of multivariate skew normal distribution (Azzalini and Dalla Valle, {\it Biometrika}, 1996), the joint distribution of a random sample from a skew-normal population can not be coherently a multivariate skew normal distribution. This incoherence causes awkwardness in the application of skew normal distribution, especially in the development of the corresponding sampling distribution theory. In this talk, we shall present a new family of multivariate skew normal distributions which embraces multivariate skew normal family defined by Azzalini and Dalla Valle (1996). The newly constructed distribution family is endowed with many statistical properties, including the coherency with the joint distribution of a set of univariate skew normal random sample. Stochastic representations for the newly defined distribution family will also be discussed.

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