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On some characterizations of spherical distributions

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  • Arellano-Valle, Reinaldo B.

Abstract

A characterization for each spherical (symmetric) distribution is presented. Moreover, a representation as a scale mixture of the Pearson type II distribution is obtained. Some extensions to the multivariate case are also considered.

Suggested Citation

  • Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:3:p:227-232
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    References listed on IDEAS

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    1. Volodin, Nikolai A., 1999. "Spherically Symmetric Logistic Distribution," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 202-206, August.
    2. Khatri, C. G. & Mukerjee, Rahul, 1987. "Characterization of normality within the class of elliptical contoured distributions," Statistics & Probability Letters, Elsevier, vol. 5(3), pages 187-190, April.
    3. Liang, Jia-Juan & Bentler, Peter M., 1998. "Characterizations of some subclasses of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 155-164, September.
    4. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    5. Bansal, N. & Hamedani, G. G. & Key, Eric S. & Volkmer, Hans & Zhang, Hao & Behboodian, J., 1999. "Some characterizations of the normal distribution," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 393-400, May.
    6. R. Arellano-Valle & H. Bolfarine & P. Iglesias, 1994. "A predictivistic interpretation of the multivariatet distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(2), pages 221-236, December.
    7. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Jolanta Misiewicz & Jacek Wesołowski, 2012. "Winding planar probabilities," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 507-519, May.
    2. Arellano-Valle, R.B. & del Pino, G. & Iglesias, P., 2006. "Bayesian inference in spherical linear models: robustness and conjugate analysis," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 179-197, January.
    3. Arellano-Valle, Reinaldo B. & Ferreira, Clécio S. & Genton, Marc G., 2018. "Scale and shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 98-110.

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