On the asymptotic behavior the powers of tests based on the samples with random sizes

Recieved: 09/07/2025

Accepted: 10/16/2025

Keywords: power of test, level, asymptotic deficiency, hypotheses testing, efficiency, sample with random size, random index, asymptotic expansions, truncated Poisson and binomial distributions

To cite this article

Bening V.E. On the asymptotic behavior the powers of tests based on the samples with random sizes. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2026. N 1, p.3-13 https://doi.org/10.55959/MSU/0137–0782–15–2026–50–1–3–13.

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Bening V.E. (Lomonosov Moscow State University (MSU))

Abstract

The paper considers the asymptotic behaviour of the distribution functions of the statistics based on the samples with random sizes in the testing problems conserning univariate parameters. An asymptotic comparison of the tests is carried out in terms of the necessary additional number of such factors (asymptotic deficiency). Two examples illustrating the obtained results are presented. These examples concern truncated Poisson and binomial distributions are considered.