ABSTRACT
In this chapter, the authors deal with the question of how to obtain random variables from non-uniform distributions. They describe a method that provides approximations to random variables which are discrete but that take on infinite number of possible values. The authors provide exact methods for generating some of most important such random variables. The Box-Muller transformation method for generating normal random variables is suggestive of methods the readers will now use for a number of distributions. If it is known from mathematical statistics that distribution the readers wish to generate can be obtained through transformation of random variables that the readers already know how to generate, this immediately furnishes an algorithm for generating the new distribution. However, the square of a standard normal random variable is a chi-square random variable with one degree of freedom. The sum of independent chi-square random variables is chi-square, with degrees of freedom the sum of the degrees of freedom of the variables summed.
