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Register a new userA Note on the Existence of the Multivariate Gamma Distribution
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Thomas Royen
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The p-variate gamma distribution in the sense of Krishnamoorthy and Parthasarathy exists for all positive integer degrees of freedom d and at least for all real values d > p-2, p > 1. For special structures of the associated covariance matrix it also exists for all positive d. In this paper a relation between central and non-central multivariate gamma distributions is shown, which implies the existence of the p-variate gamma distribution at least for all non-integer d greater than the integer part of (p-1)/2 without any additional assumptions for the associated covariance matrix.
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