LAUSR

We consider methods for numerical evaluation of the probability density function, cumulative distribution function and quantile function of a linear combination of n independent generalized logistic random variables. Here we derive the exact expressions for the probability density function and cumulative distribution function in terms of Fox's H-function. We also provide an algorithm for numerical calculation of Fox H- function and we compare its performance with a method based on the numerical inversion of the characteristic function. The numerical precision, efficiency and computing time of the proposed algorithm were considered. Applicability and comparison of the suggested approaches are illustrated by an application to financial returns.