Pade approximations of probability density functions

The analysis of radar detection systems often requires extensive knowledge of the special functions of applied mathematics, and their computation. Yet, the moments of the detection random variable are often easily obtained. We demonstrate here how to employ a limited number of exactly specified moments to approximate the probability density and distribution functions of various random variables. The approach is to use the technique of Pade approximations (PA) which creates a pole-zero model of the moment generating function (mgf). This mgf is inverted using residues to obtain the densities