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THE EXACT DISTRIBUTION OF INDEFINITE QUADRATIC

FORMS IN NONCENTRAL NORMAL VECTORS

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SERGE B. PROVOST AND EDMUND M. RUDIUK

*Department of Statistical and Actuarial Sciences, The
University
of Western Ontario,*

London, Ontario, Canada N6A 5B7
(Received March 29, 1994; revised August 7, 1995)

**Abstract.**
The exact density of the difference of two
linear combinations of independent noncentral chi-square variables
is obtained in terms of Whittaker's function and expressed in closed
forms. Two distinct representations are required in order to cover
all the possible cases. The corresponding expressions for the exact
distribution function are also given.

*Key words and phrases*:
Exact distribution function,
exact density function, indefinite quadratic forms, noncentral
chi-square variables, singular normal vectors, Whittaker's function.

**Source**
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