Recovering a probability density function from its Mellin transform

The recovering of a probability density function f(x) from its Mellin trans form M(s) is considered. The approximate f(M)(x) is chosen resorting to max imum entropy technique constrained by the first derivatives of M(s) evaluat ed at s = 1. So the basic properties of a probability density are saved. Existence conditions of the approximate f(M)(x), entropy-convergence and th en L-1-norm convergence are proved. Some numerical examples are reported. R esorting to the Mellin transform is an alternative to Laplace one, as the r ecovered probability distribution is heavy-tailed, or equivalently its prob ability density function has abscissa convergence Laplace transform equal t o 0. (C) 2001 Elsevier Science Inc. All rights reserved.