  We use a Stein identity to define a new class of parametric distributions
which we call ``independent additive weighted bias distributions.'' We
investigate related $L^2$-type discrepancy measures, empirical versions of
which not only encompass traditional ODE-based procedures but also offer novel
methods for conducting goodness-of-fit tests in composite hypothesis testing
problems. We determine critical values for these new procedures using a
parametric bootstrap approach and evaluate their power through Monte Carlo
simulations. As an illustration, we apply these procedures to examine the
compatibility of two real data sets with a compound Poisson Gamma distribution.
