Distribution of joint run-lengths of bivariate Markov processes

Abstract

Abstract Joint negative run-length characterizes the duration of drought occurring simultaneously at two locations. Probability distributions of joint negative run-lengths are derived for stationary bivariate processes which are both serially and mutually dependent. The dependence is assumed to be Markovian. It is found that joint negative run-lengths are distributed geometrically with a parameter that depends on the correlation coefficients and the truncation level. Results are compared with approximate expressions given by other authors. Derived equations are applied to monthly and annual flow records, and the agreement is found to be reasonably good.