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

Article
  • 117 Downloads

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  

Supplementary material

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

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

Personalised recommendations