Computational probability applications

Abstract

There is a boundary separating analytic methodology and simulation methodology. If a problem involves the flipping of coins or the rolling of dice, for example, analytic methods are generally employed. If a problem involves a complex series of queues with a nonstationary arrival stream, discrete-event simulation methods are generally employed. This tutorial considers problems that are near the boundary between analytic methods and simulation methods. We use the Maple-based APPL (A Probability Programming Language) to perform operations on random variables to address these problems. The problems considered are the infinite bootstrap, the probability distribution of the Kolmogorov-Smirnov test statistic, the distribution of the time to complete a stochastic activity network, finding a lower bound on system reliability, Benford's law, finding the probability distribution and variance-covariance matrix of sojourn times in a queueing model, probability distribution relationships, testing random numbers, bivariate transformations, and autoregressive moving average time series models.