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On the stochastic ordering of waiting times for patterns in sequences of random digits

Published online by Cambridge University Press:  14 July 2016

Gunnar Blom
Gunnar Blom*
Affiliation:
University of Lund
*
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 725, S-220 07 Lund, Sweden.
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Abstract

Random digits are collected one at a time until a pattern with given digits is obtained. Blom (1982) and others have determined the mean waiting time for such a pattern. It is proved that when a given pattern has larger mean waiting time than another pattern, then the waiting time for the former is stochastically larger than that for the latter. An application is given to a coin-tossing game.

Keywords

COIN-TOSSING GAMEGENERATING FUNCTIONLEADING NUMBERSLEADING QUANTITYOVERLAP
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 730 - 737
Copyright
Copyright © Applied Probability Trust 1984 

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References

Blom, G. (1982) On the mean number of random digits until a given sequence occurs. J. Appl. Prob. 19, 136–143.Google Scholar
Blom, G. and Thorburn, D. (1982) How many random digits are required until given sequences are obtained? J. Appl. Prob. 19, 518–531.Google Scholar
Chen, R. and Zame, A. (1979) On fair coin-tossing games. J. Multivariate Anal. 9, 150–156.Google Scholar
Li, S. R. (1980) A martingale approach to the study of occurrence of sequence patterns in repeated experiments. Ann. Prob. 8, 1171–1176.CrossRefGoogle Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar