The paper develops new methods of non-parametric estimation a compound
Poisson distribution. Such a problem arise, in particular, in the inference of
a Levy process recorded at equidistant time intervals. Our key estimator is
based on series decomposition of functionals of a measure and relies on the
steepest descent technique recently developed in variational analysis of
measures. Simulation studies demonstrate applicability domain of our methods
and how they positively compare and complement the existing techniques. They
are particularly suited for discrete compounding distributions, not necessarily
concentrated on a grid nor on the positive or negative semi-axis. They also
give good results for continuous distributions provided an appropriate
smoothing is used for the obtained atomic measure
