Premium
EXPRESSIONS FOR INVERSE MOMENTS OF POSITIVE QUADRATIC FORMS IN NORMAL VARIABLES
Author(s) -
Jones M. C.
Publication year - 1986
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.1986.tb00604.x
Subject(s) - quadratic equation , mathematics , inverse , computation , moment (physics) , inverse function , function (biology) , quadratic form (statistics) , quadratic function , calculus (dental) , statistics , algorithm , physics , medicine , geometry , dentistry , classical mechanics , evolutionary biology , biology
Summary A unified approach to the provision of exact expressions for inverse moments of positive quadratic forms in normal variables is described, using the method of (essentially) integrating the moment‐generating‐function (Cressie, Davis, Folks & Policello (1981). A number of special cases, many familiar from the literature, are reviewed; some allow closed form representations, others are expressed in terms of well‐known mathematical functions. In the general case, our approach affords representations suitable for numerical computations.