The distributions of the sliding block patterns in finite samples and the inclusion-exclusion principles for partially ordered sets (Probability Symposium)

Abstract

The sliding block patterns are the random variables that count the number of the appearance of words in finite samples. In this paper we show a new formula of the distributions of sliding block patterns for Bernoulli processes with finite alphabet. In particular we show a new inclusionexclusion principle on partially ordered sets with multivariate generating function, and give a simple formula of the distribution of the sliding block patterns with generating functions. We also show the formula of higher moments of the sliding block patterns. By comparing the powers of tests, we show the significant performance of the sliding block patterns tests. We show that the sliding block patterns tests reject the BSD Library RNG with p-value almost zero.