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A note on domains of attraction of p-max stable laws

Author

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  • Christoph, Gerd
  • Falk, Michael

Abstract

A distribution function (df) F is said to belong to the p-max domain of attraction of a nondegenerate df G, iff there exist [alpha]n > 0, [beta]n > 0 such that the df Fn([alpha]n x [beta]n sign(x)) converges weakly to G. The class of possible limiting dfs G and their domains of attraction are characterized by results from classical extreme value theory. This main result unifies earlier ones obtained by Pantcheva et al.

Suggested Citation

  • Christoph, Gerd & Falk, Michael, 1996. "A note on domains of attraction of p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 279-284, July.
  • Handle: RePEc:eee:stapro:v:28:y:1996:i:3:p:279-284
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    References listed on IDEAS

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    1. Subramanya, U. R., 1994. "On max domains of attraction of univariate p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 271-279, March.
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    Cited by:

    1. Feng, Bo & Chen, Shouquan, 2015. "On large deviations of extremes under power normalization," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 27-35.
    2. AL-Hussaini, Essam K. & El-Adll, Magdy E., 2004. "Asymptotic distribution of normalized maximum under finite mixture models," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 109-117, October.
    3. Chen, Shouquan & Wang, Chao & Zhang, Geng, 2012. "Rates of convergence of extreme for general error distribution under power normalization," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 385-395.
    4. Barakat, H.M. & El-Adll, Magdy E., 2009. "Asymptotic theory of extreme dual generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1252-1259, May.
    5. E. Nigm, 2006. "Bootstrapping extremes of random variables under power normalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 257-269, June.
    6. repec:eee:stapro:v:130:y:2017:i:c:p:25-31 is not listed on IDEAS
    7. H. Barakat & E. Nigm & Magdy El-Adll, 2010. "Comparison between the rates of convergence of extremes under linear and under power normalization," Statistical Papers, Springer, vol. 51(1), pages 149-164, January.

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