Geodesic
Application of Smirnov words to waiting time distributions of runs
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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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.
DOI : 10.37236/5753
Classification : 05A05, 05A15, 60C05, 60G40, 68R10
Mots-clés : waiting time distribution, run, Smirnov word, generating function 
@article{10_37236_5753,
     author = {Uta Freiberg and Clemens Heuberger and Helmut Prodinger},
     title = {Application of {Smirnov} words to waiting time distributions of runs},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {3},
     doi = {10.37236/5753},
     zbl = {1369.05006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5753/}
}
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Uta Freiberg; Clemens Heuberger; Helmut Prodinger. Application of Smirnov words to waiting time distributions of runs. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/5753

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