APPROXIMATING PROBABILITY DISTRIBUTION FUNCTIONS WITH FEW MOMENTS

A procedure is presented for approximating a given probability distribution function or statistical data considering a subset of their moments.This is done by a method of fitting moments of a piecewise linear functionto the moments of the known data. The approach has many advantages over popular approximation approaches. The procedure is demonstrated with commonly used cdfs (Exponential, Gamma, Log-Normal, Normal) andmore difficult problems involving sum and product of random variables,obtaining good agreement between the theoretical/simulation curves and the piecewise linear approximations.

NOTE ON THE PRODUCT OF RANDOM VARIABLES

The probability distribution of the product of independent random variables is computed for some particular cases which illustrate the principle that random variables having finite probability density at the origin give rise to products having infinite probability density at the origin.