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Muliere and Scarsini's bivariate Pareto distribution: sums, products and ratios.

Saralees Nadarajah, Samuel Kotz (2005)

SORT

We derive the exact distributions of R = X + Y, P = X Y and W = X / (X + Y) and the corresponding moment properties when X and Y follow Muliere and Scarsini's bivariate Pareto distribution. The expressions turn out to involve special functions. We also provide extensive tabulations of the percentage points associated with the distributions. These tables -obtained using intensive computer power- will be of use to the practitioners of the bivariate Pareto distribution.

Multidimensional Heisenberg convolutions and product formulas for multivariate Laguerre polynomials

Michael Voit (2011)

Colloquium Mathematicae

Let p,q be positive integers. The groups U p ( ) and U p ( ) × U q ( ) act on the Heisenberg group H p , q : = M p , q ( ) × canonically as groups of automorphisms, where M p , q ( ) is the vector space of all complex p × q matrices. The associated orbit spaces may be identified with Π q × and Ξ q × respectively, Π q being the cone of positive semidefinite matrices and Ξ q the Weyl chamber x q : x x q 0 . In this paper we compute the associated convolutions on Π q × and Ξ q × explicitly, depending on p. Moreover, we extend these convolutions by analytic continuation to series of convolution...

Multipliers of Laplace transform type for Laguerre and Hermite expansions

Pablo L. De Nápoli, Irene Drelichman, Ricardo G. Durán (2011)

Studia Mathematica

We present a new criterion for the weighted L p - L q boundedness of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we recover known results on weighted estimates for Laguerre and Hermite fractional integrals with a unified and simpler approach.

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