The residual effect of a growth‐decay mechanism and the distributions of covariance structures | Zendy

Mathai A.M. | Zendy

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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.

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