Application of Smirnov Words to Waiting Time Distributions of Runs

  • Uta Freiberg
  • Clemens Heuberger
  • Helmut Prodinger
Keywords: Waiting time distribution, Run, Smirnov word, Generating function.


Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed $h$-run of any letter (i.e., first occurrence of $h$ subsequential equal letters) is computed. The expected waiting time for the completion of $h$-runs of $j$ arbitrary distinct letters is also given.

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