THE MEAN WAITING TIME FOR A PATTERN
Probability in the Engineering and Informational Sciences
Probability in the Engineering and Informational Sciences
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We are interested in E [N], the mean time until the most recent k values of a sequence of independent and identically distributed random variables exceeds a specified constant. Using recent results, we present a simulation procedure for determining E [N]. These results are also used to obtain upper and lower bounds for E [N]. These bounds, however, are in terms of a quantity &ohgr; that is not easily calculated. A recursive procedure for evaluating &ohgr; when the data distribution is Bernoulli is given. Efficient simulation procedures for estimating &ohgr; in the cases of normal and exponential population distributions are also presented, as is a Markov chain monte carlo procedure when the distribution is general.