ABSTRACT
Chapter 6 served as a brief review of the theory of runs, or the consecutive occurrence of events in a sequence of Bernoulli trials. During this process we developed a family of difference equations denoted by Ri,k(n). From this family of equations, we were able to compute the probability distribution of the number of failure runs of a given length. With access to hydrology data from the state of Texas, we were able to verify that the distribution of drought lengths observed in Texas in the early to middle 20th century was what we might predict from the Ri,k(n) model. This was a gratifying finding since we were particularly concerned about the applicability of the assumption of applying independence across Bernoulli trials to the model.
