CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2012, 28(6) 637-646 DOI:      ISSN: 1001-4268 CN: 31-1256

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Some Properties of g-Covariance and g-Correlation Coefficient

Hao Tao

School of Science and Technology, Shandong University of Traditional Chinese Medicine

Abstract��

A new nonlinear covariance based on
-expectation, -covariance, is introduced and some properties
of -covariance including commutativity, homogeneity, additivity
are studied. According to these results, the sufficient and
necessary condition of -covariance satisfied homogeneity and
additivity is obtained. That is , a linear function of .
Correlation coefficient based on -expectation does not rang from
-1 to 1 and it does not reflect the linear relationship between
two random variables, either.

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