Run Probabilities in Sequences of Markov-Dependent Trials

Steven J. Schwager
1983 Journal of the American Statistical Association  
The probability of the occurrence of a run R is obtained as a function of the composition of R, the number n of trials, and the probabilities of the v :l!: 2 possible outcomes at each trial. The run R can consist of any specified sequence of outcomes, and the probability that one or more of a given collection of runs occurs is also evaluated. The probabilities of the v possible outcomes can vary arbitrarily from trial to trial, and can be L-order Markov dependent on the L preceding outcomes.
more » ... ceding outcomes. The practical application of these results is discussed. The author wishes to thank Barry Margolin, Steven Ostro,-and Douglas Robson for helpful discussions about applications of the methods of this paper.
doi:10.1080/01621459.1983.10477947 fatcat:ihrii6jrwvc7vlv2kdfzcr4lxu