Theory and Applications of Elliptically Contoured and Related Distributions
STANFORD UNIV CA DEPT OF STATISTICS
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A random vector X is said to have elliptically contoured distribution if it has the distribution of micron AY, where micron is a constant matrix, and the random vector Y has a spherical distributed that is, Y is distributed as QY for every orthogonal matrix Q. This paper surveys recent work on distribution theory and statistical inference for elliptically contoured distributions. It emphasizes the contributions of the authors and of the students and associates of the second author it gives a picture of this area of multivariate analysis that is particularly active in the Peoples Republic of China. Included are classifications of elliptically contoured and related distributions, distributions of quadratic forms, estimation of parameters, testing hypotheses, and applications. Since the normal distribution is in the class, the properties of elliptically contoured distributions are similar to those of the normal distribution.
- Statistics and Probability