TY - JOUR
T1 - New scaling model for variables and increments with heavy-tailed distributions
AU - Riva, Monica
AU - Neuman, Shlomo P.
AU - Guadagnini, Alberto
N1 - Publisher Copyright:
© 2015. American Geophysical Union. All Rights Reserved.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - 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, ΔY. Whereas distributions of Y (or its logarithm) are at times slightly asymmetric with relatively mild peaks and tails, those of ΔY 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 ΔY 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 ΔY as well as corresponding lead statistical moments. In our model the peak and tails of the ΔY 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 ΔY. We illustrate key features of our new model and method of inference on synthetically generated samples and neutron porosity data from a deep borehole.
AB - 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, ΔY. Whereas distributions of Y (or its logarithm) are at times slightly asymmetric with relatively mild peaks and tails, those of ΔY 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 ΔY 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 ΔY as well as corresponding lead statistical moments. In our model the peak and tails of the ΔY 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 ΔY. We illustrate key features of our new model and method of inference on synthetically generated samples and neutron porosity data from a deep borehole.
KW - heavy-tailed distributions
KW - neutron porosity
KW - parameter estimation
KW - scaling
KW - sub-Gaussian
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U2 - 10.1002/2015WR016998
DO - 10.1002/2015WR016998
M3 - Article
AN - SCOPUS:84937521622
SN - 0043-1397
VL - 51
SP - 4623
EP - 4634
JO - Water Resources Research
JF - Water Resources Research
IS - 6
ER -