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Convergence of distributions of extremal independent random variables

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Literature Cited

  1. A. Aksomaitis, “Nonuniform estimate of the rate of convergence in the transfer theorem for extremal values,” Liet. Mat. Rinkinys,27, No. 2, 219–223 (1987).

    Google Scholar 

  2. A. Aksomaitis, “Nonuniform rate of convergence in the limit theorem for the max-scheme,” Liet. Mat. Rinkinys,28, No. 2, 211–215 (1988).

    Google Scholar 

  3. Ya. Galambosh, Asymptotic Theory of Extremal Order Statistics [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  4. B. V. Gnedenko, “Sur la distribution limite du terme maximum d'une serie aleatoire,” Ann. Math.,44, 423–453 (1943).

    Google Scholar 

  5. B. V. Gnedenko and D. B. Gnedenko, “Laplace and logistic distributions as limits in probability theory,” Serdika,8, 229–234 (1982).

    Google Scholar 

  6. V. M. Zolotarev, Modern Theory of Summation of Independent Random Variables [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  7. E. Pancheva, “Characterization of the class of ML-laws under nonlinear normalization,” Teor. Veroyatn. Primen.,30, No. 4, 601–602 (1985).

    Google Scholar 

  8. E. Pancheva, “General limit theorems for the maximum of independent random variables,” Teor. Veroyatn. Primen.,31, No. 4, 730–744 (1986).

    Google Scholar 

  9. I. S. Shiganov, “Analogies in the study of stability in various schemes of transformation of random variables,” Teor. Veroyatn. Primen.,28, No. 4, 818–819 (1983).

    Google Scholar 

  10. I. P. Cohen, “Convergence rates for the ultimate and penultimate approximation in extreme-value theory,” Adv. Appl. Probab.,14, 833–854 (1982).

    Google Scholar 

  11. M. Falk, “Rates of uniform convergence of extreme order statistics,” Ann. Inst. Statist. Math.,38, Part A, 245–262 (1986).

    Google Scholar 

  12. E. Pancheva, “Limit theorems for extreme order statistics under non-linear normalization,” Lect. Notes Math.,1151, 284–309 (1985).

    Google Scholar 

  13. S. I. Resnick, “Uniform rates of convergence to extreme value distributions,” Technical Report, Colorado State Univ. (1985).

  14. R. L. Smith, “Uniform rates of convergence in extreme value theory,” Adv. Appl. Probab.,14, 600–622 (1982).

    Google Scholar 

  15. S. B. Weinstein, “Theory and application of some classical and generalized asymptotic distributions of extreme value,” IEEE Trans. Inf. Theory,19, 148–154 (1973).

    Google Scholar 

  16. V. M. Zolotarev and S. T. Rachev, “Rate of convergence in limit theorems for the maxscheme,” Lect. Notes Math.,1155, 415–442 (1985).

    Google Scholar 

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Kaunas Polytechnic Institute. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 30, No. 2, pp. 219–232, April–June, 1990.

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Aksomaitis, A. Convergence of distributions of extremal independent random variables. Lith Math J 30, 87–96 (1990). https://doi.org/10.1007/BF00970835

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  • DOI: https://doi.org/10.1007/BF00970835

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