Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database

Abstract

In extreme excess modeling, one fits a generalized Pareto (GP) distribution to rainfall excesses above a properly selected threshold u. The latter is generally determined using various approaches, such as nonparametric methods that are intended to locate the changing point between extreme and nonextreme regions of the data, graphical methods where one studies the dependence of GP‐related metrics on the threshold level u, and Goodness‐of‐Fit (GoF) metrics that, for a certain level of significance, locate the lowest threshold u that a GP distribution model is applicable. Here we review representative methods for GP threshold detection, discuss fundamental differences in their theoretical bases, and apply them to 1714 overcentennial daily rainfall records from the NOAA‐NCDC database. We find that nonparametric methods are generally not reliable, while methods that are based on GP asymptotic properties lead to unrealistically high threshold and shape parameter estimates. The latter is justified by theoretical arguments, and it is especially the case in rainfall applications, where the shape parameter of the GP distribution is low; i.e., on the order of 0.1–0.2. Better performance is demonstrated by graphical methods and GoF metrics that rely on preasymptotic properties of the GP distribution. For daily rainfall, we find that GP threshold estimates range between 2 and 12 mm/d with a mean value of 6.5 mm/d, while the existence of quantization in the empirical records, as well as variations in their size, constitute the two most important factors that may significantly affect the accuracy of the obtained results.

Sensitivity of flood frequency analysis to data record, statistical model, and parameter estimation methods: An evaluation over the contiguous United States

“…Identification of the appropriate threshold is not a straightforward task and still remains an issue of uncertainty in PDS estimates (Langousis, Mamalakis, Puliga, & Deidda, 2016). An appropriate threshold should be high enough to represent the tail of the distribution and, at the same time, the retained data should provide an increased data sample with respect to the AMS (Caballero-Megido, Hillier, Wyncoll, Bosher, & Gouldby, 2018).…”

A parametric approach for simultaneous bias correction and high‐resolution downscaling of climate model rainfall

“…The only difference between parametric distribution mapping and its empirical variant described in the previous section is that in the parametric approach F m , k and F H, k in equations and are not the empirical CDFs, but theoretical distribution models properly fitted to data. Suggested distributions in the literature for daily rainfall include the exponential, gamma, lognormal, and the generalized Pareto (GP) models [see e.g., Langousis and Veneziano , ; Piani et al ., ; Deidda , ; Gutjahr and Heinemann , ; Langousis and Kaleris , ; Papalexiou et al ., ; Serinaldi and Kilsby , ; Langousis et al ., ], with the latter being used to model rainfall excesses above some sufficiently high threshold value u * .…”

“…The applicability of the generalized Pareto (GP) distribution to parameterize the upper tail of the empirical distribution of rainfall has been verified both theoretically and empirically [see e.g., Balkema and de Haan , ; Pickands , ; Leadbetter et al ., ; Smith , ; Leadbetter , ; Stedinger et al ., ; Coles , ; Martins and Stedinger , , ; Deidda and Puliga , ; Deidda , ; Papalexiou et al ., ; Serinaldi and Kilsby , ; Langousis et al ., ]. To model low rainrates, we use an exponential distribution, as the simplest parametric form that belongs to the GP family.…”

Serviceability assessment for long-span suspension bridge based on deflection measurements

“…The threshold selection requires consideration of the trade‐off between bias and variance: A too high threshold reduces the number of exceedances and thus increases the estimated variance, whereas a low threshold can reduce the estimated variance but increase the bias . In order to find a proper threshold u , several statistical methods have been proposed, which can be grouped into three categories: (a) nonparametric methods that locate the changing point between extreme and nonextreme regions of the data; (b) graphical methods that search for the linear behavior of the GPD parameters (or related metrics) with the increasing threshold; and (c) goodness‐of‐fit tests that locate the lowest threshold u that a GPD model is applicable for any given level of significance …”