Abstract
We introduce some new classes of unimodal rotational invariant directional distributions, which generalize von Mises–Fisher distribution. We propose three types of distributions, one of which represents axial data. For each new type we provide formulae and short computational study of parameter estimators by the method of moments and the method of maximum likelihood. The main goal of the paper is to develop the goodness of fit test to detect that sample entries follow one of the introduced generalized von Mises–Fisher distribution based on the maximum entropy principle. We use kth nearest neighbour distances estimator of Shannon entropy and prove its -consistency. We examine the behaviour of the test statistics, find critical values and compute power of the test on simulated samples. We apply the goodness of fit test to local fiber directions in a glass fibre reinforced composite material and detect the samples which follow axial generalized von Mises–Fisher distribution.
Acknowledgment
The authors are grateful to Prof. Katja Schladitz for the help with the real data, Martin Gurka and Sebastian Nissle (Institut für Verbundwerkstoffe, Kaiserslautern) for permission to reuse the tomographic images, Prof. Claudia Redenbach for providing the data set of fiber directions. We would like to thank the Editor, Domenico Marinucci, and the anonymous referee for their insightful comments and suggestions, that led to an improvement of a previous version of this work.
Citation
Nikolai Leonenko. Vitalii Makogin. Mehmet Siddik Cadirci. "The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond." Electron. J. Statist. 15 (2) 6344 - 6381, 2021. https://doi.org/10.1214/21-EJS1946
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