A measure of monotonicity of two random variables

Simple item page
aut.relation.endpage228
aut.relation.issue2
aut.relation.startpage221
aut.relation.volume8
aut.researcherKachapova, Farida
dc.contributor.authorKachapova, F
dc.contributor.authorKachapov, I
dc.date.accessioned2013-06-07T07:24:32Z
dc.date.available2013-06-07T07:24:32Z
dc.date.copyright2012
dc.date.issued2012
dc.description.abstractProblem 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.identifier.citationJournal of Mathematics and Statistics, vol.8(2), pp.221 - 228
dc.identifier.doi10.3844/jmssp.2012.221.228
dc.identifier.issn1549-3644
dc.identifier.urihttps://hdl.handle.net/10292/5424
dc.publisherScience Publications
dc.relation.urihttp://dx.doi.org/10.3844/jmssp.2012.221.228
dc.rightsCompliance 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.rights.accessrightsOpenAccess
dc.subjectMonotonicity
dc.subjectComonotonic
dc.subjectCounter-monotonic
dc.subjectMonotone dependence
dc.subjectMeasure of dependence
dc.subjectPearson correlation
dc.subjectBivariate distributions
dc.subjectRandom variables
dc.titleA measure of monotonicity of two random variables
dc.typeJournal Article
pubs.elements-id113656
pubs.organisational-data/AUT
pubs.organisational-data/AUT/Design & Creative Technologies
pubs.organisational-data/AUT/Design & Creative Technologies/School of Computing & Mathematical Science
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