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CONVERGENT SERIES EXPRESSIONS FOR INVERSE MOMENTS OF QUADRATIC FORMS IN NORMAL VARIABLES
Author(s) -
Smith Murray D.
Publication year - 1988
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1988.tb00854.x
Subject(s) - mathematics , inverse , quadratic equation , scalar (mathematics) , mathematical analysis , series (stratigraphy) , invariant (physics) , quadratic form (statistics) , multivariate normal distribution , multivariate statistics , combinatorics , mathematical physics , statistics , paleontology , geometry , biology
Summary Using relatively recent results from multivariate distribution theory, a direct approach to evaluating the inverse moments of a quadratic form in normal variables is proposed. Convergent infinite series expressions involving the invariant polynomials of matrix argument are obtained. The solution also depends upon a positive scalar which is arbitrarily chosen. For the solution to converge an upper bound upon this scalar is derived.