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General max-stable laws

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Abstract

We review the work on max-stable laws and their max domains of attraction introduced by Pancheva (Lect Notes Math 1155:284–309, 1984). We introduce the concept of general max domain of strict attraction of the general max-stable laws, a subclass of the general max domain of attraction and prove new results. Some interesting examples also are discussed.

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References

  • Aczel, J.: Lectures in Functional Equations and Their Applications. Academic, New York (1966)

    Google Scholar 

  • Christoph, G., Falk, M.: A note on domain of attraction of p-max stable laws. Stat. Probab. Lett. 28, 279–284 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  • de Haan, L.: A spectral representation for max-stable processes. Ann. Probab. 12, 1194–1204 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  • de Haan, L.: A unified criterion for the domain of attraction of extreme-value distributions. Theory Probab. Appl. 39, 323–329 (1994)

    Article  MathSciNet  Google Scholar 

  • de Haan, L., Resnick, S.I.: Limit theory for multivariate sample extremes. Z. Wahrsch. verw. Gebiete 40, 317–333 (1977)

    Article  MATH  Google Scholar 

  • Galambos, J.: The Asymptotic Theory of Extreme Order Statistics. Wiley, New York (1978)

    MATH  Google Scholar 

  • Kunin, B.: A new type of extreme value distributions. Eng. Fract. Mech. 58, 557–570 (1997)

    Article  Google Scholar 

  • Kunin, B.: Extreme value type distributions with bounded support. Int. J. Pure Appl. Math. 12, 499–513 (2004)

    MATH  MathSciNet  Google Scholar 

  • Marshall, A.W., Olkin, I.: Domains of attraction of multivariate extreme value distributions. Ann. Probab. 11, 168–177 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • Mohan, N.R., Ravi, S.: Max domains of attraction of univariate and multivariate p-max stable laws. Theory Probab. Appl. 37, 632–643 (1992)

    Article  MathSciNet  Google Scholar 

  • Pancheva, E.: Limit theorems for extreme order statistics under nonlinear normalization. Lect. Notes Math. 1155, 284–309 (1984)

    Article  MathSciNet  Google Scholar 

  • Pancheva, E.: Max-stability. Theory Probab. Appl. 33, 155–158 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • Pancheva, E.: Selfdecomposable distributions for maxima of independent random vectors. Probab. Th. Rel. Fields 84, 267–278 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • Pancheva, E.: Extreme value limit theory with nonlinear normalization. In: Galambos, J., et al. (eds.) Extreme Value Theory and Applications, pp. 305–318. Kluwer, Boston (1994)

    Google Scholar 

  • Ravi, S.: Power normalization and p-max stable laws. In: Falk, M., et al. (eds.) Laws of Small Numbers-Extremes and Rare Events, DMV Seminar, vol. 23, 2nd edn., pp. 64–74. Birkhaeuser, Basel (2004)

    Google Scholar 

  • Resnick, S.I.: Extreme Values, Regular Variation and Point Processes. Springer, New York (1987)

    MATH  Google Scholar 

  • Tiago de Oliveira, J.: Bivariate and multivariate extremal distributions. In: Patil, G. P., et al. (eds.) Statistical Distributions in Scientific Work, vol. 1, pp. 355–361. Riedel, Dordrecht (1975)

    Google Scholar 

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  1. Department of Statistics, M. S. University of Baroda, 6-B, Vrundavan Park, New Sama Road, Vadodara, 390008, India

    M. Sreehari

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  1. M. Sreehari
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Sreehari, M. General max-stable laws. Extremes 12, 187–200 (2009). https://doi.org/10.1007/s10687-008-0074-2

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  • DOI: https://doi.org/10.1007/s10687-008-0074-2

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