The Bessel function expression of characteristic function

In this article, we give a unified method to derive the classical characteristic functions of all elliptical and related distributions in terms of Bessel functions. The approach is based on the stochastic representation of an elliptical random variable and the characteristic function of uniform distribution on the unit sphere surface in ℝn. In particular, we present the simple closed form of characteristic functions for commonly used distributions such as multivariate t, Pearson Type II, Pearson Type VII, Kotz type, and Bessel distributions. Some extensions are also being investigated.

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