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

TL;DR

This paper derives new formulas for the distribution of sliding block patterns in finite samples of Bernoulli processes, introduces an inclusion-exclusion principle for partially ordered sets, and explores statistical testing power.

Contribution

It presents a novel inclusion-exclusion formula in multivariate generating function form and simplifies the expression of generating functions for pattern occurrences.

Findings

Distribution formulas for sliding block patterns in finite samples

New inclusion-exclusion principle for partially ordered sets

Higher moments and test power analysis

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.