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Characteristic functions of a class of elliptical distributions. (English) Zbl 0816.62040

Summary: The Kotz-type distributions form an important class of multivariate elliptical distributions. These distributions are studied by K.-T. Fang et al. [Symmetric multivariate and related distributions. (1990; Zbl 0699.62048), Chap. 3.2]. In the particular case when the shape parameter \(s\) equals 1, S. Iyengar and Y. L. Tong [Sankhyā, Ser. A 51, No. 1, 13-29 (1989; Zbl 0673.62043)] determined explicitly the characteristic function of the distributions. F. Streit [C. R. Math. Acad. Sci., Soc. R. Can. 13, No. 4, 121-124 (1991; Zbl 0752.60016)] derived a general formula for the characteristic functions valid for all \(s > 1/2\). 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.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E10 Characteristic functions; other transforms
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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