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Limit Distributions of a Random Term of a Variational Series

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There are a lot of papers devoted to the study of order statistics, in particular, the asymptotics of the kth term of a variational series for a sample of size n of independent identically distributed random variables with distribution F(x) with different relations between k and n. In the “central” part, where min(k, n − k) → ∞, the normal limit distribution dominates. In the present paper we study the asymptotic behavior of a random term of the variational series: its number ν is a random variable, taking values 1, 2,…, n with equal probabilities. Under mild assumptions on the density of underlying distribution, we find all possible limit distributions for the νth term of variational series.

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Authors and Affiliations

  1. Regional Social Foundation “Informatics for Democracy”, Moscow, Russia

    Yu. N. Blagoveschenskiy

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  1. Yu. N. Blagoveschenskiy
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Correspondence to Yu. N. Blagoveschenskiy.

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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 19, pp. 105–117, 2006

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Blagoveschenskiy, Y.N. Limit Distributions of a Random Term of a Variational Series. J Math Sci 220, 672–681 (2017). https://doi.org/10.1007/s10958-016-3210-6

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  • DOI: https://doi.org/10.1007/s10958-016-3210-6

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