  In this work we derive an inversion formula for the Laplace transform of a
density observed on a curve in the complex domain, which generalizes the well
known Post-Widder formula. We establish convergence of our inversion method and
derive the corresponding convergence rates for the case of a Laplace transform
of a smooth density. As an application we consider the problem of statistical
inference for variance-mean mixture models. We construct a nonparametric
estimator for the mixing density based on the generalized Post-Widder formula,
derive bounds for its root mean square error and give a brief numerical
example.
