Numerical Methods for Approximating Continuous Probability Density Functions, over [0, {infty}), Using Moments

Three numerical methods are presented for the reconstructionof a continuous probability density function f(x) from givenvalues of the moments of the distribution. The first methodis obtained by assuming that f(x) may be expanded as an infiniteseries of generalized Laguerre polynomials . The use of ordinary Laguerre polynomials, corresponding to theparticular choice = 0, is related to a second method involvingthe numerical inversion of a Laplace transform. In the thirdmethod the principle of maximization of entropy, subject tothe known moment constraints, is used to reconstruct f(x). Thetype of fit to be expected from each method is illustrated bynumerical examples.