Abstract
In recent years there has been much attention to the analysis and comparison of different measures of similarity and dissimilarity of probability distributions. In this work, we consider such measures as functions defined on the set of probability distributions and satisfying given properties. Further, we consider a correlation function defined on the set of probability distributions and satisfying simple properties fulfilled for most of the known correlation and association coefficients considered in statistics. We discuss general methods of constructing correlation functions from similarity and dissimilarity functions. Finally, we introduced several new similarity, dissimilarity, and correlation functions on the set of probability distributions.
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Acknowledgements
The work was done with partial support from the Mexican Government through grant A1-S-47854 of CONACYT, Mexico, and grants SIP 20220857, 20211874, 20220852, and 20220859 of the Instituto Politecnico Nacional, Mexico. The authors acknowledge the support of Microsoft through the Microsoft Latin America Ph.D. Award.
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Ensastegui-Ortega, M.E., Batyrshin, I., Gelbukh, A. (2023). On Similarity Correlation of Probability Distributions. In: Shahbazova, S.N., Abbasov, A.M., Kreinovich, V., Kacprzyk, J., Batyrshin, I.Z. (eds) Recent Developments and the New Directions of Research, Foundations, and Applications. Studies in Fuzziness and Soft Computing, vol 422. Springer, Cham. https://doi.org/10.1007/978-3-031-20153-0_19
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DOI: https://doi.org/10.1007/978-3-031-20153-0_19
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