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On the distribution of quadratic forms in normal random variables
Author(s) -
Tan W. Y.
Publication year - 1977
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 - 10.2307/3314784
Subject(s) - mathematics , quadratic equation , extension (predicate logic) , random variable , square (algebra) , distribution (mathematics) , chi square test , normal distribution , quadratic form (statistics) , noncentral chi squared distribution , statistics , mathematical analysis , asymptotic distribution , ratio distribution , geometry , computer science , estimator , programming language
This paper provides necessary and sufficient conditions for a quadratic form in singular normal random variables to be distributed as a given linear combination of independent noncentral chi‐square variables. Using this result, an extension of Cochran's theorem to quadratic forms of noncentral chi‐square variables is derived.