Entropy-based test for generalized Gaussian distributions

Cadirci, Mehmet Siddik; Evans, D. Gareth; Leonenko, Nikolai; Makogin, Vitalii

doi:10.48550/arxiv.2010.06284

Cited by 2 publications

(3 citation statements)

References 19 publications

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“…We apply Theorem 4.5. Repeating the lines of the proof of (Cadirci et al, 2020, Theorem 3), we compute E[ξ (0, P λ )], where…”

Section: Entropy Estimationmentioning

confidence: 99%

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The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond

Leonenko¹,

Makogin²,

Cadirci³

2020

Preprint

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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 L 2 -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.

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“…We apply Theorem 4.5. Repeating the lines of the proof of (Cadirci et al, 2020, Theorem 3), we compute E[ξ (0, P λ )], where…”

Section: Entropy Estimationmentioning

confidence: 99%

“…Lund & Jammalamadaka (2000) considered the entropy based test of goodness of fit for the von Mises distribution on the circle and use a different entropy estimate. Our study is motivated, particularly, by the work of Cadirci et al (2020), where the entropy based goodness of fit test for generalized Gaussian distribution is given.…”

Section: Introductionmentioning

confidence: 99%

The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond

Leonenko¹,

Makogin²,

Cadirci³

2020

Preprint

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“…The quadratic Rényi entropy was investigated by [18]. An entropy-based goodness-of-fit test for generalized Gaussian distributions is presented by [3]. A recent application to image processing can be found in [6].…”

Section: Introductionmentioning

confidence: 99%

Statistical tests based on Rényi entropy estimation

Cadirci,

Evans,

Leonenko

et al. 2021

Preprint

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Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-offit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Rényi entropy based on nearest neighbour distances. We prove the L 2 -consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods. In addition we present a novel iterative method for estimating the shape parameter of the multivariate Student and multivariate Pearson type II distributions.

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Entropy-based test for generalized Gaussian distributions

Cited by 2 publications

References 19 publications

The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond

The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond

Statistical tests based on Rényi entropy estimation

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