Modeling Precipitation Extremes using Log-Histospline
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One of the commonly used approaches to modeling univariate extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a (sufficiently high/low) threshold as a generalized Pareto distribution (GPD). This method requires the selection of a threshold that might affect the estimates. Here we propose an alternative method, the "Log-Histospline (LHSpline)", to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned histogram of the log transformed data to estimate its log density. By construction, a LHSpline estimation is constrained to have polynomial tail behavior, a feature commonly observed in geophysical observations. We illustrate LHSpline method by analyzing precipitation data collected in Houston, Texas.
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