Measuring Departure From Gaussian Assumptions In Spatial Processes

The concept of entropy is classical in thermodynamics and information theory. Its potential use as a measure of the ordering of a spatial system is discussed. Although entropy has been discussed previously in the framework of spatial statistics and for univariate distributions, a bivariate data-based estimator has not until now been defined. Different statistical distributions maximize entropy, depending on the univariate, bivariate, or n-variate constraints applied. For bivariate distributions, with a known mean and known covariance, it can be shown that the distribution that maximizes the entropy of the system is the bivariate gaussian. A nonparametric bivariate entropy estimator is introduced, derived directly from the experimental cumulative frequency distribution. Assuming that this experimental bivariate distribution is representative of the population distribution, then a measure of departure from gaussianity can be introduced as a relative entropy estimator. Practical applications for the entropy estimator are discussed, and an example developed.