Abstract
It was shown (Cifarelli and Regazzini 1987) that maximal separation of two probability measures P and Q can be assessed by a maximal concentration curve of one of the probability measures with respect to the other. In case of two univariate distributions, one can measure their monotone separation by means of a monotone concentration curve and related numerical index ar. We are extending this idea into a multivariate case. We discuss properties of a proposed index of monotone separation of multivariate distributions, especially in relation to dependence and stochastic ordering, and show examples of how the index can be used in data analysis.
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References
Agresti, A. (1984), Analysis of Ordinal Categorical Data. J. Wiley, New York.
Bamber, D. (1975), The area above the ordinal dominance graph and area below the receiver operating characteristic graph. J. Math. Psych., 12, 387–415 .
Cifarelli, D. M., and E. Regazzini (1987), On a general definition of concentration function. Sankhyā, 49, 307–319.
Gafrikova, V., and M. Niewiadomska-Bugaj (1998), On the point and interval estimation of discriminant index ar. In III Seminar on Methods of Statistical Identification. Akademia Rolnicza, Wroclaw, Poland.
Kowalczyk, T. (1999) Separability of Bivariate Distributions.
Schweizer, B., and A. Sklar (1974), Operations on distribution functions not derivable from operations on random variables. Studia Mathematica, LII, 43–52.
SAS Institute (1994), JMP Statistical Software. SAS Institute Inc., USA.
Szczesny, W. (1991), On the performance of a discriminant function. Journal of Classification, 8, 201–215.
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© 2002 Springer Science+Business Media Dordrecht
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Kowalczyk, T., Niewiadomska-Bugaj, M. (2002). A New Grade Measure of Monotone Multivariate Separability. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_15
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DOI: https://doi.org/10.1007/978-94-017-0061-0_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6136-2
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