Integral representations of one-dimensional projections for multivariate stable densities

Authors:
Muneya Matsui;Akimichi Takemura
Affiliations:
Department of Mathematics, Keio University, Japan;Graduate School of Information Science and Technology, University of Tokyo, Japan
Venue:
Journal of Multivariate Analysis
Year:
2009

Citing 6
Cited 0

Approximation of multidimensional stable densities

Journal of Multivariate Analysis
A practical guide to heavy tails: statistical techniques and applications

A practical guide to heavy tails: statistical techniques and applications
Multivariate stable densities as functions of one dimensional projections

Journal of Multivariate Analysis
On two approaches to approximation of multidimensional stable laws

Journal of Multivariate Analysis
Estimating the spectral measure of a multivariate stable distribution via spherical harmonic analysis

Journal of Multivariate Analysis
Test of association between multivariate stable vectors

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the numerical evaluation of one-dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan [H. Abdul-Hamid, J.P. Nolan, Multivariate stable densities as functions of one dimensional projections, J. Multivariate Anal. 67 (1998) 80-89]. In their approach higher order derivatives of one-dimensional densities are used, which seems to be cumbersome in practice. Furthermore there are some difficulties for even dimensions. In order to overcome these difficulties we obtain the explicit finite-interval integral representation of one-dimensional projections for all dimensions. For this purpose we utilize the imaginary part of complex integration, whose real part corresponds to the derivative of the one-dimensional inversion formula. We also give summaries on relations between various parametrizations of stable multivariate density and its one-dimensional projection.