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The residual effect of a growth‐decay mechanism and the distributions of covariance structures
Author(s) -
Mathai A.M.
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315753
Subject(s) - covariance , mathematics , bilinear interpolation , scalar (mathematics) , generalization , multivariate normal distribution , residual , class (philosophy) , laplace operator , pure mathematics , statistical physics , multivariate statistics , statistics , mathematical analysis , physics , computer science , geometry , algorithm , artificial intelligence
The product of two independent or dependent scalar normal variables, sums of products, sample covariances, and general bilinear forms are considered. Their distributions are shown to belong to a class called generalized Laplacian. A growth‐decay mechanism is also shown to produce such a generalized Laplacian. Sets of necessary and sufficient conditions are derived for bilinear forms to belong to this class. As a generalization, the distributions of rectangular matrices associated with multivariate normal random vectors are also discussed.