On a Uniqueness Property of α-Spherical Distributions

• Autorzy: Wesołowski J.
• Języki publikacji: EN

Abstrakty

EN

A distribution of an α-spherical random vector is shown to be uniquely determined by a distribution of quotients.

Słowa kluczowe

EN

α-spherical random vector; distribution of quotients; α-spherical distributions

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 1
• Strony: 123--132
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Wesołowski J.

• Mathematical Institute, Warsaw University of Technology, plac Politechniki 1, 00-661 Warsaw, Poland

Bibliografia

• [1] A. K. Gupta and D. Song, Characterization of p-generalized normality, J. Multivariate Anal. 60 (1997), pp. 61-71.
• [2] - Lp-norm uniform distribution, Proc. Amer. Math. Soc. 125 (1997), pp. 595-601.
• [3] - Lp-norm spherical distributions, J. Statist. Plann. Inference 60 (1997), pp. 241-260.
• [4] R. D. Gupta, J. K. Misiewicz and D. St. P. Richards, Infinite sequences with sign-symmetric Liouville distributions, Probab. Math. Statist. 16 (1996), pp. 29-44.
• [5] I. Kotlarski, On characterizing the gamma and the normal distribution, Pacific J. Math. 20 (1967), pp. 69-76.
• [6] R. G. Laha, An example ofa non-normal distribution where the quotient follows the Cauchy law, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), pp. 222-223.
• [7] G. Letac, Isotropy and sphericity: some characterisations of the normal distribution, Ann. Statist. 9 (1981), pp. 408-417.
• [8] W. Matysiak, A characterization of sign-symmetric Liouville-type distributions, Preprint 1-5 (1998).
• [9] V. Seshadri, A characterization of the normal and Weibull distributions, Canad. Math. Bull. 12 (1969), pp. 257-260.
• [10] P. J. Szabłowski, Uniform distributions on spheres in finite dimensional Lα, and their generalizations, J. Multivariate Anal. 64 (1998), pp. 103-117.
• [11] - J. Wesołowski and M. Ahsanullah, Identification of probability measures via distribution of quotients, J. Statist. Plann. Inference 63 (1997), pp. 377-385.
• [12] J. Wesołowski, Some characterizations connected with properties of the quotient of independent random variables, Teor. Veroyatnost. i Primenen. 36 (1991), pp. 780-781.
• [13] - A characterization of the bivariate elliptically contoured distribution, Statist. Papers 33 (1992), pp. 143-149.