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

Bruno Ebner; Yvik Swan

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arXiv · 2304.13179

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

Bruno Ebner·Yvik Swan

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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 $L^2$-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.

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Bruno Ebner, Yvik Swan. 2023-04-25. Independent additive weighted bias distributions and associated goodness-of-fit tests. https://arxiv.org/abs/2304.13179

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