Number of appearances of events in random sequences: a new generating function approach to Type II and Type III runs



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.


Runs statistics Generating function Asymptotic distributions Factorial moments Wilf-Zeilberger method  

Supplementary material (51 kb)
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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2015

Authors and Affiliations

  1. 1.Department of Molecular Biophysics and Biochemistry, W.M. Keck Foundation Biotechnology Resource LaboratoryYale UniversityNew HavenUSA

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