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Cluster Structured Multivariate Probability Distribution with Uniform Marginals

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Classification as a Tool for Research

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Abstract

Reducing the dimension of classification space we doubt if this transformation is spoiling the original group structure of the mixture generating our data. This problem can be discussed on the basis of analysis of data generated by the specific probability distributions. Denkowska and Sokolowski (1997) proposed two-dimensional probability distribution with probability distributed uniformly on two squares which size is controlled by one parameter. In this paper, the special multivariate probability distribution is proposed. In n-dimensions it has a cluster structure consisting of hypercubes but all marginal distributions are uniform.

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References

  • Denkowska, S., & Sokolowski A. (1997). O pewnym rozkladzie prawdopodobienstwa dwuwymiarowej zmiennej losowej (On a certain probability distribution of a two-dimensional random variable). Cracow University of Economics, Proceedings of 35th conference of statistics, econometrics and mathematics departments of universities of economics (pp. 59–67). Cracow.

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Author information

Authors and Affiliations

  1. Department of Statistics, Cracow University of Economics, Cracow, Poland

    Andrzej Sokolowski

Authors
  1. Andrzej Sokolowski
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  2. Sabina Denkowska
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Corresponding author

Correspondence to Andrzej Sokolowski .

Editor information

Editors and Affiliations

  1. LS für BWL, insb. Finanzwirtschaft und, Finanzdienstleistungen, TU Dresden, Helmholtzstr. 10, Dresden, 01062, Germany

    Hermann Locarek-Junge

  2. FG Computergestützte Statistik, Univ. Dortmund, Vogelpothsweg 87, Dortmund, 44227, Germany

    Claus Weihs

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Sokolowski, A., Denkowska, S. (2010). Cluster Structured Multivariate Probability Distribution with Uniform Marginals. In: Locarek-Junge, H., Weihs, C. (eds) Classification as a Tool for Research. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10745-0_22

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