Conditional Distribution of Runs and Patterns and Their Applications

• Activity Number: 340 - New Advances in Analysis of Social Science Research
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Tung-Lung Wu*
• Companies: Mississippi State University
• Keywords: finite Markov chain imbedding ; distribution-free tests ; runs and patterns ; quality control ; scan statistic ; longest run

Abstract

We study the distributions of runs and patterns in a sequence of Bernoulli trials given the number of successes (or failures). Given the number of total successes, the outcomes of a sequence of $n$ Bernoulli trials can be viewed as random permutations. This gives us distribution-free tests based on runs and patterns. Applications to statistical process control and test for randomness are given to illustrate our methods. Furthermore, we extend the results to multi-state trials.