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Limit theorems for record values using power normalization

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Abstract

The paper obtains a complete description of the limit distributions of record values of a sequence of i.i.d. random variables with common continuous distribution function F under power normalization. For each of the six types of limiting laws, we obtain criteria for F to belong to the corresponding domain of attraction as well as the form of the normalizing constants.

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References

  1. S. I. Resnick, Limit laws for record values, Stoch. Processes Appl., 1, 67–82 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  2. M. N. Tata, On outstanding values in a sequence of random variables, Z. Wahrsch. verw. Geb., 12(1), 9–20 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin (1997).

    MATH  Google Scholar 

  4. B. Grigelionis, On the extreme-value theory for stationary diffusions under power normalization, Lith. Math. J., 44(1), 44–56 (2004).

    Article  MathSciNet  Google Scholar 

  5. N. R. Mohan and S. Ravi, Max domains of attraction of univariate and multivariate p-max stable laws, Teor. Veroyatnost. i Primenen., 37(4), 709–721 (1992).

    MATH  MathSciNet  Google Scholar 

  6. E. Pantcheva, Limit theorems for extreme order statistics under nonlinear normalization, in: Lect. Notes in Math., vol. 1155, Springer, Berlin (1985), pp. 284–309.

    Google Scholar 

  7. M. Marcus and M. Pinsky, On the domain of attraction of exp{e−x}, J. Math. Anal. Appl., 28, 440–449 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  8. R. von Mises, La distribution de la plus grande de n valeurs, Revue Mathématique de l’Union Interbalkanique, 1, 141–160 (1936).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania

    B. Grigelionis

  2. Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania

    B. Grigelionis

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  1. B. Grigelionis
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Additional information

Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 492–500, October–December, 2006.

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Grigelionis, B. Limit theorems for record values using power normalization. Lith Math J 46, 398–405 (2006). https://doi.org/10.1007/s10986-006-0037-8

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  • DOI: https://doi.org/10.1007/s10986-006-0037-8

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