An analytical representation of bivariate isotropic stable density

Document Type : Research Article

Authors

Faculty of Mathematics and Computer Science, Amirkabir University of Technology

Abstract

Stable random vectors are characterized by their characteristic functions. The multivariate
 stable density and distribution functions generally do not have an analytic form. A few numerical
 methods have been developed to compute density functions of parametric stable random vectors.
 However, they have some limitations in terms of the range of the tail index. In this work, via the
 inversion formula, we present a new analytical representation of the density function of a bivariate
 isotropic stable random vector. We show that the analytical representation can be reduced to a closed
 form at the origin.

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