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On the rate of convergence in the central limit theorem

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References

  1. Amosova, N. N., On the rate of convergence of probabilities of moderate deviations under restrictions on the moments. Theor. Prob. and Math. Statist., 19(1980), 1–6.

    MATH  Google Scholar 

  2. Banys, J., Estimate of convergence rate for densities in the metric of Lp. Liet. Mat. Rinkinys, 15(1975), 5–10.

    MATH  Google Scholar 

  3. Banys, J., Refinement of rate of convergence to a stable law. Liet. Mat. Rinkinys, 16(1976), 5–22.

    MathSciNet  MATH  Google Scholar 

  4. Banys, J., Refinement of the rate of convergence of densities to the stable law with characteristic exponent 0<α<1 in the metric of Lp. Liet. Mat. Rinkinys, 18(1978), 174–178.

    MathSciNet  MATH  Google Scholar 

  5. Baum, L. E., and Katz, M. L., On the influence of moments on the asymptotic distribution of sums of random variables. Ann. Math. Stat., 34(1963), 1042–1044.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Galstjan, F. N., Local analysis of a theorem of Heyde. Soviet Math. Dokl., 12(1971), 596–600.

    Google Scholar 

  7. Galstjan, F. N., On asymptotic expansions in the central limit theorem. Theory Prob. Appl., 16(1971), 528–533.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Galstjan, F. N., On the rate of convergence in the central limit theorem. Theor. Prob. and Math. Statist., 5 (1975), 13–24.

    MathSciNet  Google Scholar 

  9. Heyde, C. C., On the influence of moments on the rate of convergence to the normal distribution. Z. Wahrscheinlichkeitstheorie, 8(1967), 12–18.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Heyde, C. C., Some properties of metrics in a study on convergence to normality. Z. Wahrscheinlichkeitstheorie, 11(1969), 181–192.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Heyde, C. C., and Leslie, J. R., On the influence of moments on approximations by portion of a Chebyshev series in central limit convergence. Z. Wahrscheinlichkeitstheorie, 21(1972), 255–268.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Ibragimov, I. A., and Linnik, Yu. V., Independent and stationary sequences of random variables. Wolters-Noordhoff, Groningen 1971.

    Google Scholar 

  13. Loève, M., Probability Theory. D. Van Nostrand, Princeton 1963.

    MATH  Google Scholar 

  14. Petrov, V. V., Sums of Independent Random Variables. Springer-Verlag, New York 1975.

    CrossRef  MATH  Google Scholar 

  15. Rohatgi, V. K., Convergence to normality in L1-metric. Bull. Inst. Math. Acad. Sinica, 4(1976), 83–86.

    MathSciNet  MATH  Google Scholar 

  16. Rohatgi, V. K., Asymptotic expansions in a local limit theorem. Colloquia Mathematica Societas János Bolyai, Vol. 21, ed. B. Gyires, North-Holland 1979, 307–315.

    Google Scholar 

  17. Rychlik, Z., and Szynal, D., Convergence rates in the central limit theorem for sums of a random number of independent random variables. Teor. Veroyatnost. Primen., 20(1975), 359–370.

    MathSciNet  MATH  Google Scholar 

  18. Serova, G. V., On the rate of convergence in the central limit theorem. Theor. Prob. and Math. Statist., 17(1979), 121–130.

    MATH  Google Scholar 

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© 1981 Springer-Verlag

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Rohatgi, V.K. (1981). On the rate of convergence in the central limit theorem. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097321

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  • DOI: https://doi.org/10.1007/BFb0097321

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10823-8

  • Online ISBN: 978-3-540-36785-7

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