g-协方差和g-相关系数的几个性质

Some Properties of g-Covariance and g-Correlation Coefficient

  • 摘要: 介绍一类建立在-期望基础之上新的非线性协方差----协方差. 研究了-协方差的几个性质, 包括交换性、齐次性、可加性. 在此基础上还得到当-协方差同时满足齐次性和可加性的充要条件, 即关于是线性的. 发现基于-期望的相关系数的值不介于之间, 且它也不再反映两个随机变量间的线性关系.

     

    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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