Supplement to the law of large numbers when extreme terms are excluded

  • Hirohisa Hatori
  • Makoto Maejima
  • Toshio Mori
Article
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Keywords

Stochastic Process Probability Theory Mathematical Biology Extreme Term 

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References

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    Hatori, H., Maejima, M., Mori, T.: Convergence rates in the law of large numbers when extreme terms are excluded. Z. Wahrscheinlichkeitstheorie verw. Gebiete 47, 9 (1979)Google Scholar
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    Heyde, C.C., Rohatgi, V.K.: A pair of complementary theorems on convergence rates in the law of large numbers. Proc. Camb. Phil. Soc. 63, 73–82 (1967)Google Scholar
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    Mori, T.: The strong law of large numbers when extreme terms are excluded from sums. Z. Wahrscheinlichkeitstheorie verw. Gebiete 36, 189–194 (1976)Google Scholar
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    Petrov, V.V.: One-sided law of large numbers for ruled sums. (In Russian) Vestnik Leningrad. Univ. 1974, 55–59 (1974)Google Scholar
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    Zolotarev, V.: On some Cebyšev type inequalities in one-sided sense. (In Russian) Litovsk. Mat. Sb. 5, 233–250 (1965)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Hirohisa Hatori
    • 1
  • Makoto Maejima
    • 2
  • Toshio Mori
    • 3
  1. 1.Department of MathematicsScience University of TokyoTokyoJapan
  2. 2.Department of Mathematics, Faculty of EngineeringKeio UniversityYokohamaJapan
  3. 3.Department of MathematicsYokohama City UniversityYokohamaJapan

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