An algorithm to compute the probability of a run in binary fourth-order Markovian trials

In this paper we give an algorithm that may be used to compute the probability of the occurrence of a given number of consecutive successes (or failures) in binary trials that are dependent. The dependence structure is assumed to be Markovian of order four. The algorithm is applied to the analysis of start-up demonstration test data and to computing the probability of rainy periods in Fort Lauderdale, Florida. The importance of choosing a correct model order and the usefulness of the algorithm for making this choice are illustrated.