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New scaling model for variables and increments with heavy‐tailed distributions
Author(s) -
Riva Monica,
Neuman Shlomo P.,
Guadagnini Alberto
Publication year - 2015
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr016998
Subject(s) - statistical physics , logarithm , heavy tailed distribution , mathematics , scaling , gaussian , probability density function , probability distribution , statistical parameter , distribution (mathematics) , random variable , statistics , physics , mathematical analysis , geometry , quantum mechanics
Abstract 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, Δ Y . Whereas distributions of Y (or its logarithm) are at times slightly asymmetric with relatively mild peaks and tails, those of Δ 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 Δ 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 Δ Y as well as corresponding lead statistical moments. In our model the peak and tails of the Δ 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 Δ 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.