Selecting series size where the generalized Pareto distribution best fits

Rates of arrival and magnitudes of hydrologic variables are frequently described by the Poisson and the generalized Pareto (GP) distributions. Variations of their goodness-of-fit to nested series are studied here. The variable employed is depth of rainfall events at five stations of the Israel Meteorological Service. Series sizes range from about 50 (number of years on records) to about 1000 (total number of recorded events). The goodness-of-fit is assessed by the Anderson-Darling test. Three versions of this test are applied here. These are the regular two-sided test (of which the statistic is designated here by A2), the upper one-sided test (UA2) and the adaptation to the Poisson distribution (PA2). Very good fits, with rejection significance levels higher than 0.5 for A2 and higher than 0.25 for PA2, are found for many series of different sizes. Values of the shape parameter of the GP distribution and of the predicted rainfall depths widely vary with series size. Small coefficients of variation are found, at each station, for the 100-year rainfall depths, predicted through the series with very good fit of the GP distribution. Therefore, predictions through series of very good fit appear more consistent than through other selections of series size. Variations of UA2, with series size, are found narrower than those of A2. Therefore, it is advisable to predict through the series of low UA2. Very good fits of the Poisson distribution to arrival rates are found for series with low UA2. But, a reversed relation is not found here. Thus, the model of Poissonian arrival rates and GP distribution of magnitudes suits here series with low UA2. It is recommended to predict through the series, to which the lowest UA2 is obtained.