Run Probabilities in Sequences of Markov-Dependent Trials

Abstract

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 ≥ 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. The practical application of these results is discussed.

Key Words:

• Runs tests
• Runs distributions
• Multiple Markov dependence
• Time-dependent trials