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Some families of mutivariate symmetric distributions related to exponential distribution

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  • Fang, Kai-Tai
  • Fang, Bi-Qi

Abstract

This paper introduces a family of multivariate symmetric distributions, which includes the one with i.i.d. exponential components as its special member. This family, denoted by Fn, is defined as scale mixtures of the uniform distribution on the surface of the l1 unit sphere and studied from several aspects such as distribution functions, probability density functions, marginal and conditional distributions and components' independence. A more general family Tn in which the survival functions are functions in l1 norm and an important subset Dn,[infinity] of scale mixtures of random vector with i.i.d. exponential components are also discussed. The relationships among these three families and some applications are given.

Suggested Citation

  • Fang, Kai-Tai & Fang, Bi-Qi, 1988. "Some families of mutivariate symmetric distributions related to exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 109-122, January.
    • Handle: RePEc:eee:jmvana:v:24:y:1988:i:1:p:109-122
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    Citations

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    Cited by:

    1. Yue, Xinnian & Ma, Chunsheng, 1995. "Multivariate p-norm symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 281-288, September.
    2. Qu, Xiaomei & Zhou, Jie & Shen, Xiaojing, 2010. "Archimedean copula estimation and model selection via l1-norm symmetric distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 406-414, April.
    3. Jiajuan Liang & Kai-Tai Fang & Fred Hickernell, 2008. "Some necessary uniform tests for spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 679-696, September.
    4. Hélène Cossette & Etienne Marceau & Quang Huy Nguyen & Christian Y. Robert, 2019. "Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 461-490, June.
    5. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
    6. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    7. Yanqin Fan & Marc Henry, 2020. "Vector copulas," Papers 2009.06558, arXiv.org, revised Apr 2021.
    8. Claude Lefèvre & Matthieu Simon, 2021. "Schur-Constant and Related Dependence Models, with Application to Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 317-339, March.
    9. Ng, Kai Wang & Tian, Guo-Liang, 2001. "Characteristic Functions of 1-Spherical and 1-Norm Symmetric Distributions and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 192-213, February.
    10. Fang, B. Q., 2002. "Estimation of the location parameter of the l1-norm symmetric matrix variate distributions," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 269-280, April.

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