  The problem of parameter estimation by observations of inhomogeneous Poisson
processes is considered. The method of moments estimator is studied and its
stochastic expansion is obtained. This stochastic expansion is then used to
obtain the expansion of the moments of this estimator and the expansion of the
distribution function. The stochastic expansion, expansion of the moments and
the expansion of distribution function are non asymptotic in nature. Several
examples are considered.
