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Conditional limiting distribution of beta-independent random vectors

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  • Hashorva, Enkelejd

Abstract

The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m =0, such that W2 is a beta distributed random variable with parameters m/2,(d-m)/2 and (U1,...,Um),(Um+1,...,Ud) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors.

Suggested Citation

  • Hashorva, Enkelejd, 2008. "Conditional limiting distribution of beta-independent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1438-1459, August.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:7:p:1438-1459
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    References listed on IDEAS

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    1. Hashorva, Enkelejd, 2006. "On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 2027-2035, December.
    2. Berman, Simeon M., 1983. "Sojourns and extremes of Fourier sums and series with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 213-238, August.
    3. Hashorva, Enkelejd, 2005. "Extremes of asymptotically spherical and elliptical random vectors," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 285-302, June.
    4. Hashorva, Enkelejd, 2007. "Conditional limiting distribution of Type III elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 282-294, February.
    5. 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. Balakrishnan, N. & Hashorva, E., 2013. "Scale mixtures of Kotz–Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 48-58.
    2. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
    3. Balakrishnan, N. & Hashorva, E., 2011. "On Pearson-Kotz Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 948-957, May.
    4. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
    5. Vladimír Lacko & Radoslav Harman, 2012. "A conditional distribution approach to uniform sampling on spheres and balls in L p spaces," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 939-951, October.
    6. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.

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