Characteristic Functions of a Class of Elliptic Distributions

The Kotz-type distributions form an important class of multivariate elliptical distributions. These distributions are studied in Fang et al. [Symmetric Multivariate and Related Distributions, Chap. 3.2. Chapman and Hall, London]. In the particular case when the shape parameters s equals 1, Iyengar and Tong [Sankhya Ser. A51 13-29 ] determined explicitly the characteristic function of the distributions. Streit [C.R. Math. Rep. Acad. Sci. Canada13 121-124] derived a general formula for the characteristic functions valid for all s > 12. In the present paper, the structure of the characteristic functions for a Kotz-type multivariate distribution for all values of the parameters is obtained. The relationship to the characteristic function of a lognormal distribution is noted.