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

Abstract: In this paper we show the distributions of sliding block patterns for Bernoulli processes with finite alphabet, which is not based on the induction on sample size. We show a new inclusion-exclusion formula in multivariate generating function form on partially ordered sets, and show a simpler expression of generating functions of the number of pattern occurrences in finite samples. We show higher moments of the sliding block patterns and power of tests based on sliding block patterns.