  One of the commonly used approaches to modeling extremes is the
peaks-over-threshold (POT) method. The POT method models exceedances over a
threshold that is sufficiently high or low so that the exceedance has
approximately 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 daily rainfall observations. We
illustrate the LHSpline method by analyzing precipitation data collected in
Houston, Texas.
