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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 $U_{p} (ℂ)$ and $U_{p} (ℂ) \times U_{q} (ℂ)$ act on the Heisenberg group $H_{p, q} : = M_{p, q} (ℂ) \times ℝ$ canonically as groups of automorphisms, where $M_{p, q} (ℂ)$ is the vector space of all complex p × q matrices. The associated orbit spaces may be identified with $Π_{q} \times ℝ$ and $Ξ_{q} \times ℝ$ respectively, $Π_{q}$ being the cone of positive semidefinite matrices and $Ξ_{q}$ the Weyl chamber $x \in ℝ^{q} : x ₁ \geq \dots \geq x_{q} \geq 0$ . In this paper we compute the associated convolutions on $Π_{q} \times ℝ$ and $Ξ_{q} \times ℝ$ explicitly, depending on p. Moreover, we extend these convolutions by analytic continuation to series of convolution...

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Monodromy of hypergeometric functions and non-lattice integral monodromy

Monodromy of the hypergeometric differential equation of type (3,6) II. The unitary reflection group of order $2^{9} . 3^{7} . 5 . 7$

Monopoles and modifications of bundles over elliptic curves.

Monotonic and logarithmically convex properties of a function involving gamma functions.

Monotonicity and bounds on Bessel functions.

Monotonicity and concavity properties of some functions involving the gamma function with applications.

Monotonicity and convexity for the gamma function.

Monotonicity of a key function arised in studies of nematic liquid crystal polymers.

Monotonicity properties of the linear combination of derivatives of some special functions

Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.

Monotonicity results for the Gamma function.

More statistics on permutation pairs.

Motzkin numbers, central trinomial coefficients and hybrid polynomials.

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

Multidimensional Heisenberg convolutions and product formulas for multivariate Laguerre polynomials

Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations

Multiple integrals and Fourier series expansions associated with hypergeometric polynomials

Multiple Series Relations Involving Hermite Polynomials

Multiple-scale analysis for Painlevé transcendents with a large parameter

Multiplication of subharmonic functions.

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