Numerical inversion of the Mellin transform on the real line for heavy-tailed probability density functions

摘要

A method for numerical inversion on the real line of the Mellin transform, without reduction of the problem to the inversion of Laplace transform is described. Maximum entropy technique is invoked in choosing the analytical form of the approximant function. Entropy-convergence and then L1-norm convergence is proved. A stability analysis in evaluating entropy and expected values is illustrated. An upper bound of the error in the expected values computation is provided in terms of entropy.