Symbolic and Numerical Computations for Distributions Involving Linear Combinations of Spacings or Exponential Variates

Abstract

In this talk, I will discuss algorithms for computing 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 algorithms to obtain the distributions of the scan statistic, the distributions of the maximum and minimum of a moving average process, the distribution of the Kolmogorov-Smirnov statistic, and exact inference based on exponential distribution for censored and progressively censored samples.