dc.contributor.author Kachapova, F dc.contributor.author Kachapov, I dc.date.accessioned 2013-06-07T07:24:32Z dc.date.available 2013-06-07T07:24:32Z dc.date.copyright 2012 dc.date.issued 2013-06-07 dc.identifier.citation Journal of Mathematics and Statistics, vol.8(2), pp.221 - 228 dc.identifier.issn 1549-3644 dc.identifier.uri http://hdl.handle.net/10292/5424 dc.description.abstract Problem statement: When analyzing random variables it was useful to measure the degree of their monotone dependence or compare pairs of random variables with respect to their monotonicity. Existing coefficients measure general or linear dependence of random variables. Developing a measure of monotonicity was useful for practical applications as well as for general theory, since monotonicity was an important type of dependence. Approach: Existing measures of dependence are briefly reviewed. The Reimann coefficient was generalized to arbitrary random variables with finite variances. Results: The article describes criteria for monotone dependence of two random variables and introduces a measure of this dependence-monotonicity coefficient. The advantages of this coefficient are shown in comparison with other global measures of dependence. It was shown that the monotonicity coefficient satisfies natural conditions for a monotonicity measure and that it had properties similar to the properties of the Pearson correlation; in particular, it equals 1 (-1) if and only if the pair X, Y was comonotonic (counter-monotonic). The monotonicity coefficient was calculated for some bivariate distributions and the sample version of the coefficient was defined. Conclusion/Recommendations: The monotonicity coefficient should be used to compare pairs of random variables (such as returns from financial assets) with respect to their degree of monotone dependence. In the problems where the monotone relation of two variables has a random noise, the monotonicity coefficient can be used to estimate variance and other central moments of the noise. By calculating the sample version of the coefficient one will quickly find pairs of monotone dependent variables in a big dataset." dc.publisher Science Publications dc.relation.uri http://dx.doi.org/10.3844/jmssp.2012.221.228 dc.rights Compliance with the open-access policy, all content published by Science Publications offers unrestricted access, distribution, and reproduction in any medium; provided the original work is correctly cited. dc.subject Monotonicity dc.subject Comonotonic dc.subject Counter-monotonic dc.subject Monotone dependence dc.subject Measure of dependence dc.subject Pearson correlation dc.subject Bivariate distributions dc.subject Random variables dc.title A measure of monotonicity of two random variables dc.type Journal Article dc.rights.accessrights OpenAccess dc.identifier.doi 10.3844/jmssp.2012.221.228 aut.relation.endpage 228 aut.relation.issue 2 aut.relation.startpage 221 aut.relation.volume 8 pubs.elements-id 113656
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