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Characteristic Functions of a Class of Elliptic Distributions

Author

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  • Kotz, S.
  • Ostrovskii, I.

Abstract

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 [Sankhy 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 > . 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.

Suggested Citation

  • Kotz, S. & Ostrovskii, I., 1994. "Characteristic Functions of a Class of Elliptic Distributions," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 164-178, April.
    • Handle: RePEc:eee:jmvana:v:49:y:1994:i:1:p:164-178
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    Cited by:

    1. Yeshunying Wang & Chuancun Yin, 2021. "A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1377-1407, December.
    2. Arslan, Olcay, 2005. "A new class of multivariate distributions: Scale mixture of Kotz-type distributions," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 18-28, November.
    3. Kotz, Samuel & Nadarajah, Saralees, 2001. "Some extremal type elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 171-182, September.
    4. Hashorva, Enkelejd, 2007. "Extremes of conditioned elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1583-1591, September.

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