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- W2082086147 abstract "Given two independent positive random variables x and y , and the independence of xy and (1 − x ) y , Tollar [1] proves that y is gamma and x is beta. He uses the involved methodology of random difference equations to prove this result. For n independent positive random variables x 2 ,…, x n , y , with the independence of (1 − x 2 − x 3 −…− x n ) y and ( x 2 y ,…, x n y ), Tollar's result [1] generalizes to the result that y is gamma and ( x 2 ,…, x n ) have a joint Dirichlet distribution. Similarly, given two independent p × p random positive definite symmetric matrices X and Y , with the independence of Y 1 2 XY 1 2 and Y 1 2 (I − X)Y 1 2 , it is proved that Y is Wishart and X is multivariate beta. Now given n independent p × p random symmetric positive definite matrices X 2 ,…, X n , Y , with the independence of (Y 1 2 X 2 Y 1 2 ,…,Y 1 2 X n Y 1 2 ) and Y 1 2 (I − X 2 − … − X n )Y 1 2 , we prove that Y is Wishart and ( X 2 ,…, X n ) have a joint multivariate Dirichlet density. We use the method of moment generating functions." @default.
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- W2082086147 date "1997-07-01" @default.
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- W2082086147 title "An n-variate characterization of the gamma and the complex Wishart densities" @default.
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- W2082086147 doi "https://doi.org/10.1016/s0893-9659(97)00070-0" @default.
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