Analogue of the Berry–Esseen inequality for the joint cumulative distribution function of several statistics

M. P. Savelov

Lomonosov Moscow State University

Abstract: We consider random vectors formed by statistics which are functions of a sample of independent random variables with a polynomial distribution; each of the statistics has one of three types. Analogues of the Berry–Esseen inequality are obtained for the joint cumulative distribution function of such vectors. The types of statistics are generalizations of the statistics used in the NIST statistical test suite.

Keywords: joint distributions of statistics, Berry–Esseen inequality, NIST STS, TestU01, summing statistics, long-block statistics, short-block statistics, goodness-of-fit tests.

UDC: 519.213.21+519.233.33

Received: 27.08.2024

DOI: 10.4213/dm1875