Summary
In this paper we extend Ruben's [4] result for quadratic forms in normal variables. He represented the distribution function of the quadratic form in normal variables as an infinite mixture of chi-square distribution functions. In the central case, we show that the distribution function of a quadratic form int-variables can be represented as a mixture of beta distribution functions. In the noncentral case, the distribution function presented is an infinite series in beta distribution functions. An application to quadratic discrimination is given.
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Menzefricke, U. On positive definite quadratic forms in correlatedt variables. Ann Inst Stat Math 33, 385–390 (1981). https://doi.org/10.1007/BF02480949
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DOI: https://doi.org/10.1007/BF02480949