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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
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.