V. E. Bening, N. K. Galieva, V. Yu. Korolev, “Asymptotic expansions for the distribution functions of statistics constructed from samples with random sizes”, Inform. Primen., 2013, Volume 7, Issue 2,Pages <nobr>75

This article is cited in 7 papers

Asymptotic expansions for the distribution functions of statistics constructed from samples with random sizes

V. E. Bening^ab, N. K. Galieva^c, V. Yu. Korolev^ab

^a Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University
^b IPI RAN
^c Kazakhstan Branch of Lomonosov Moscow State University

Abstract: A general transfer tteorem is proved making it possible to construct asymptotic expansions for the distribution function of a statistic constructed from the sample with a random size from the asymptotic expansion for the distribution function of the random sample size and the asymptotic expansion for the distribution function of the same statistic constructed from the samples with a nonrandom size.

Keywords: sample with a random size; asymptotic expansion; transfer theorem; mixture of probability distributions; Laplace distribution; Student distribution.