Recovering a probability density function from its Mellin transform

摘要

The recovering of a probability density function f(x) from its Mellin transform M(s) is considered. The approximate fM(x) is chosen resorting to maximum entropy technique constrained by the first derivatives of M(s) evaluated at s=1. So the basic properties of a probability density are saved.Existence conditions of the approximate fM(x), entropy-convergence and then L1-norm convergence are proved. Some numerical examples are reported. Resorting to the Mellin transform is an alternative to Laplace one, as the recovered probability distribution is heavy-tailed, or equivalently its probability density function has abscissa convergence Laplace transform equal to 0.