Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions
Copyright policy )Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions
(~'/z)~/2 x~-le --~':~-~+~ (x>0) , (1) 2 K ~ ( ] / ~ ) has the property of infinite divisibility. It follows simply from this that any mixture of the r-dimensional normal distributions Nr(~, X) determined by setting ~ = # + ~ 2 f i A and X=a2A (2) and letting o -2 follow the distribution (1) is infinitely divisible; here #, fl and A are new parameters, # and fi being r-dimensional vectors while 3 is a positive definite r x r matrix with determinant IA I = 1. This class of mixtures includes the r-dimensional hyperbolic distribution
- Aarhus University Denmark
Finite Divisibility, Student Distribution, Generalized Inverse Gaussian Distribution, Infinitely divisible distributions; stable distributions, Hyperbolic Distribution
Finite Divisibility, Student Distribution, Generalized Inverse Gaussian Distribution, Infinitely divisible distributions; stable distributions, Hyperbolic Distribution
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