New scaling model for variables and increments with heavy-tailed distributions

作者：Riva Monica^*; Neuman Shlomo P; Guadagnini Alberto

来源：Water Resources Research, 2015, 51(6): 4623-4634.

DOI：10.1002/2015WR016998

Many hydrological (as well as diverse earth, environmental, ecological, biological, physical, social, financial and other) variables, Y, exhibit frequency distributions that are difficult to reconcile with those of their spatial or temporal increments, Y. Whereas distributions of Y (or its logarithm) are at times slightly asymmetric with relatively mild peaks and tails, those of Y tend to be symmetric with peaks that grow sharper, and tails that become heavier, as the separation distance (lag) between pairs of Y values decreases. No statistical model known to us captures these behaviors of Y and Y in a unified and consistent manner. We propose a new, generalized sub-Gaussian model that does so. We derive analytical expressions for probability distribution functions (pdfs) of Y and Y as well as corresponding lead statistical moments. In our model the peak and tails of the Y pdf scale with lag in line with observed behavior. The model allows one to estimate, accurately and efficiently, all relevant parameters by analyzing jointly sample moments of Y and Y. We illustrate key features of our new model and method of inference on synthetically generated samples and neutron porosity data from a deep borehole.

• 出版日期2015-6