Performances of some parameter estimators of the generalized Pareto distribution over rounded-off samples

Recent analyses on some daily rainfall time series highlighted the presence of records with anomalous rounding (1 and 5 mm), while the standard resolution should be 0.1 or 0.2 mm. Assuming that the generalized Pareto distribution (GPD) can reliably represent the distribution of daily rainfall depths, this study investigates how such discretizations can affect the inference process. The performances of several GPD estimators are compared using the Monte Carlo approach. Synthetic samples are drawn by GPDs with shape and scale parameters in the ranges of values estimated on daily rainfall depth time series. Results show how the relative efficiency of estimators could be very different for continuous or rounded-off samples. Moreover, when the rounding-off magnitude becomes larger than a few millimeters, all the considered estimators reveal very poor performances.