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.
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Provost, S.B., Rudiuk, E.M. The exact distribution of indefinite quadratic forms in noncentral normal vectors. Ann Inst Stat Math 48, 381–394 (1996). https://doi.org/10.1007/BF00054797
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DOI: https://doi.org/10.1007/BF00054797