The average or expectation of an engineering observation random quantity is the first order origin moment. The deviation of random variable from the average is called error. The quantity used to measure the degree of correlation between the errors of two variables is covariance. Variance is a special case of covariance, when two variables are the same. The variance is the second-order central moment. The normalization of covariance to standard deviation is Pearson correlation coefficient. The normalization of variance to expectation is index of dispersion, and the derivative of the index of dispersion to the observation time interval of the accumulation span plus one then divided by two is Hurst index. The Hurst value reflects the long memory fluctuation. By making integer order moment fractional, we can have more fun, and it is called Steed version of everything said!

Hyper Covariance