Finding Probability Distributions From Moments

Using the moment sequence of a continuous probability function to regenerate the full distribution is a mathematical problem that has been investigated for many years. One method is to use a flexible distribution to approximate the densities by matching the moments of the two distributions. The results are of great interest, as they can be readily applied to response time analysis in concurrent systems, where obtaining moments is relatively easy but obtaining full distributions is hard. In this dissertation we look at the development of a tool that approximates densities when given the first four moments. The Generalized Lambda Distribution will be discussed in detail and we shall investigate the effectiveness of using it to approximate densities of well known probability distributions in addition to densities derived from response time analysis models.