Application of number theory in mathematical statistics

Yu. V. Linnik

V. A. Steklov Mathematics Institute, Leningrad Branch, Academy of Sciences of the USSR

Abstract: Elementary number theory (divisibility theory) is used to prove that, in the case of repeated sampling, when the $k$-th generalized sample moment is independent of the sample mean then the sampling is normal if the volume of the sample is large and $k$ is a square-free integer which, if it is even, is not of the form $2(2s +1)$).

UDC: 519.2

Received: 16.12.1969

 English version: Mathematical Notes, 1970, 7:4, 230–233

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