COMPUTING THE JOINT DISTRIBUTION OF GENERAL LINEAR COMBINATIONS OF SPACINGS OR EXPONENTIAL VARIATES

We present an algorithm for computing exact expressions for the distribution of the maximum or minimum of an arbitrary finite collection of linear combinations of spacings or exponential random variables with rational coefficients. These expressions can then be manipulated or evaluated using symbolic math packages such as Maple. As examples, we apply this algorithm to obtain the distributions of the maximum and minimum of a moving average process, and the distribution of the Kolmogorov-Smirnov statistic.