New estimates are obtained for the rate of convergence of the negative binomial distribution with parameters (r, p) to the gamma-distribution with parameters (r, r) when p → 0. The main result is a considerable improvement of convergence rate estimates for regular statistics constructed from samples with negatively binomially distributed random sizes to the Student distribution.
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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 19, pp. 118–134, 2006
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Gavrilenko, S.V., Zubov, V.N. & Korolev, V.Y. The Rate of Convergence of the Distributions of Regular Statistics Constructed from Samples with Negatively Binomially Distributed Random Sizes to the Student Distribution. J Math Sci 220, 701–713 (2017). https://doi.org/10.1007/s10958-016-3213-3
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DOI: https://doi.org/10.1007/s10958-016-3213-3