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Multinomial interpoint distances

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Abstract

We explore the properties of the squared Euclidean interpoint distances (IDs) drawn from multinomial distributions. We consider the distances within one sample and across two samples and obtain their means, variances, covariances and distributions. We discuss applications of IDs for testing goodness of fit, the equality of high dimensional multinomial distributions, classification, and outliers detection. A simulation study compares the performance of the \(\chi ^2\) and the likelihood ratio statistics for testing equality of distributions, with methods based on the IDs.

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Acknowledgments

I would like to thank an anonymous referees whose helpful comments and suggestions improved the presentation of the article.

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  1. Department of Statistics, The George Washington University, Washington, DC, 20052, USA

    Reza Modarres

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  1. Reza Modarres
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Correspondence to Reza Modarres.

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Modarres, R. Multinomial interpoint distances. Stat Papers 59, 341–360 (2018). https://doi.org/10.1007/s00362-016-0766-7

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  • DOI: https://doi.org/10.1007/s00362-016-0766-7

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