Number of appearances of events in random sequences: a new generating function approach to Type II and Type III runs
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Distributions of runs of length at least k (Type II runs) and overlapping runs of length k (Type III runs) are derived in a unified way using a new generating function approach. A new and more compact formula is obtained for the probability mass function of the Type III runs.
KeywordsRuns statistics Generating function Asymptotic distributions Factorial moments Wilf-Zeilberger method
This work was supported in part by the Clinical and Translational Science Award UL1 RR024139 from the National Center for Research Resources, National Institutes of Health.
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