CHARACTERISTIC FUNCTIONS OF A CLASS OF ELLIPTIC DISTRIBUTIONS

The Kotz-type distributions form an important class of multivariate el liptical 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. A 51 13-29 ] determined expl icitly the characteristic function of the distributions. Streit [CR. M ath. Rep. Acad. Sci. Canada 13 121-124] derived a general formula for the characteristic functions valid for all s > 1/2. In the present pap er, the structure of the characteristic functions for a Kotz-type mult ivariate distribution for all values of the parameters is obtained. Th e relationship to the characteristic function of a lognormal distribut ion is noted. (C) 1994 Academic Press, Inc.