Independent additive weighted bias distributions and associated goodness-of-fit tests

04/25/2023

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by   Bruno Ebner, et al.

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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.