Modeling of Stochastic Behaviors
Ken Chen · 2015
This chapter first examines the techniques allowing one to generate random variables (r.v.) that are uniformly distributed on the interval (0, 1), from which one can generate r.v. of any other distribution. It then presents some methods for generating r.v. of a given distribution from the r.v. of U(0, 1), before presenting the use and generation of some commonly used distributions. Accordingly, the distribution is known by its cumulative distribution function (CDF) for the inverse transformation method or by its probability density function (pdf) for the acceptance–rejection method. The chapter deals with the case of discrete r.v., as well as the composition and convolution of r.v. It gives a short survey and some samples models related to computer networks. The chapter also briefly discusses how to find an adequate probability distribution for a given stochastic behavior, i.e. the issue of parameter estimation and hypothesis testing.