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Independent additive weighted bias distributions and associated goodness-of-fit tests (2304.13179v1)
Published 25 Apr 2023 in stat.ME
Abstract: We use a Stein identity to define a new class of parametric distributions which we call ``independent additive weighted bias distributions.'' We investigate related $L2$-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.