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Teor. Veroyatnost. i Primenen., 1993, Volume 38, Issue 4, Pages 787–799 (Mi tvp4015)  

This article is cited in 12 scientific papers (total in 12 papers)

Domains of attraction of the max-semistable laws under linear and power normalizations

I. V. Grinevich

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider the domains of attraction of the univariate semi-stable laws in the scheme of cumulative maxima of independent identically distributed random variables and obtain necessary and sufficient conditions for a nondegenerate distribution function to belong to the domain of attraction of a max-semistable law under linear and power normalization. These theorems include the well-known criteria for belonging to the domains of attraction of max-stable laws as a special case; examples are given. The relation between the domains of attraction under linear and power normalization is shown.

Keywords: domain of attraction, max-stable law, max-semistable law, linear and power normalization.

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English version:
Theory of Probability and its Applications, 1993, 38:4, 640–650

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Received: 22.02.1993

Citation: I. V. Grinevich, “Domains of attraction of the max-semistable laws under linear and power normalizations”, Teor. Veroyatnost. i Primenen., 38:4 (1993), 787–799; Theory Probab. Appl., 38:4 (1993), 640–650

Citation in format AMSBIB
\by I.~V.~Grinevich
\paper Domains of attraction of the max-semistable laws under linear and power normalizations
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 4
\pages 787--799
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 4
\pages 640--650

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    This publication is cited in the following articles:
    1. Megyesi Z., “Domains of geometric partial attraction of max–semistable laws: Structure, merge and almost sure limit theorems”, Journal of Theoretical Probability, 15:4 (2002), 973–1005  crossref  mathscinet  zmath  isi
    2. Theory Probab. Appl., 51:2 (2007), 291–304  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Becker-Kern P., “Almost sure limit theorems of mantissa type for semistable domains of attraction”, Acta Mathematica Hungarica, 114:4 (2007), 301–336  crossref  mathscinet  zmath  isi
    4. Gomes M.I., Canto e Castro L., Fraga Alves M.I., Pestana D., “Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions”, Extremes, 11:1 (2008), 3–34  crossref  mathscinet  zmath  isi
    5. Canto e Castro L., Dias S., “Asymptotic distribution of certain statistics relevant to the fitting of max-semistable models”, Portugaliae Mathematica, 66:3 (2009), 401–412  isi
    6. Canto e Castro L., Dias S., “Generalized Pickands' estimators for the tail index parameter and max-semistability”, Extremes, 14:4 (2011), 429–449  crossref  isi
    7. Canto e Castro L., Dias S., Ternido Maria da Graca, “Looking for max-semistability: A new test for the extreme value condition”, J Statist Plann Inference, 141:9 (2011), 3005–3020  crossref  isi
    8. Freitas A., Huesler J., Temido M.G., “Limit laws for maxima of a stationary random sequence with random sample size”, Test, 21:1 (2012), 116–131  crossref  isi
    9. Hall A. Temido Maria da Graca, “On the Maximum of Periodic Integer-Valued Sequences with Exponential Type Tails via Max-Semistable Laws”, J. Stat. Plan. Infer., 142:7 (2012), 1824–1836  crossref  isi
    10. Beirlant J., Caeiro F., Ivette Gomes M., “An Overview and Open Research Topics in Statistics of Univariate Extremes”, REVSTAT-Stat. J., 10:1 (2012), 1+  isi
    11. Gomes M.I., Guillou A., “Extreme Value Theory and Statistics of Univariate Extremes: a Review”, Int. Stat. Rev., 83:2 (2015), 263–292  crossref  isi
    12. Dias S., Temido Maria Da Graca, “Random Fields and Random Sampling”, Kybernetika, 55:6 (2019), 897–914  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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