Runs and patterns with applications

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The proposed research program is a continuation of the applicant's current research on the distribution theory of runs and patterns, and on its applications to biomedical research. In general, both long- and short-term objectives are to develop theoretical foundations for various commonly used statistics that are based on runs and patterns, and to use the developed theory for statistical inference in practical applications. The specific aims for the proposed funding period include: (i) deriving the exact distribution for the length of the longest common subsequence (LCS) among two multi-state biological sequences, (ii) developing a run-length model for monitoring emergency room (ER) waiting times, and (iii) extending the applicant's previous work on compound patterns in multi-state trials under non-overlap counting to study the asymptotic properties of large samples.