On Occurrences ofF-SStrings in Linearly and Circularly Ordered Binary Sequences
Frosso S. Makri · Journal of Applied Probability · 2010
Consider a sequence of exchangeable or independent binary trials ordered on a line or on a circle. The statistics denoting the number of times anF-Sstring of length (at least)k1+k2, that is, (at least)k1failures followed by (at least)k2successes innsuch trials, are studied. The associated waiting time for therth occurrence of anF-Sstring of length (at least)k1+k2in linearly ordered trials is also examined. Exact formulae, lower/upper bounds and approximations are derived for their distributions. Mean values and variances of the number of occurrences ofF-Sstrings are given in exact formulae too. Particular exchangeable and independent sequences of binary random variables, used in applied research, combined with numerical examples clarify further the theoretical results.