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Crossing Theory for Non‐Gaussian Stochastic Processes With an Application to Hydrology
Author(s) -
Desmond A. F.,
Guy B. T.
Publication year - 1991
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 - 10.1029/91wr01745
Subject(s) - skewness , gaussian , statistical physics , gaussian process , log normal distribution , series (stratigraphy) , mathematics , streamflow , econometrics , marginal distribution , stochastic process , statistics , geology , geography , random variable , physics , quantum mechanics , drainage basin , paleontology , cartography
The theoretical properties of level crossings for stationary Gaussian processes have been applied in the past to model empirical crossing behavior of streamflow data with some success. However, when the marginal distributions exhibit departures from normality, such as high coefficients of skewness, the theoretical Gaussian results perform poorly in modeling empirical crossing behavior. In this paper we present theoretical results for crossings of levels by two non‐Gaussian processes, namely, the chi‐square process and the lognormal process. The chi‐square process does not appear to have been applied previously in the hydrologic literature. We apply both models to a skewed annual flow series. Comparisons with the Gaussian model are made and noticeable improvements are found in both cases.