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

Article

Abstract

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.

Keywords

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

Notes

Acknowledgments

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.

Supplementary material

10463_2015_549_MOESM1_ESM.mw (51 kb)
Supplementary material 1 (mw 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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