  For parameter estimation of continuous and discrete distributions, we propose
a generalization of the method of moments (MM), where Stein identities are
utilized for improved estimation performance. The construction of these
Stein-type MM-estimators makes use of a weight function as implied by an
appropriate form of the Stein identity. Our general approach as well as
potential benefits thereof are first illustrated by the simple example of the
exponential distribution. Afterward, we investigate the more sophisticated
two-parameter inverse Gaussian distribution and the two-parameter
negative-binomial distribution in great detail, together with illustrative
real-world data examples. Given an appropriate choice of the respective weight
functions, their Stein-MM estimators, which are defined by simple closed-form
formulas and allow for closed-form asymptotic computations, exhibit a better
performance regarding bias and mean squared error than competing estimators.
