scholarly journals On the suitability of the generalized Pareto to model extreme waves

2018 ◽  
Vol 56 (6) ◽  
pp. 755-770 ◽  
Author(s):  
Rui Teixeira ◽  
Maria Nogal ◽  
Alan O'Connor
Author(s):  
Philip Jonathan ◽  
Kevin Ewans

The characteristics of extreme waves in hurricane dominated regions vary systematically with a number of covariates, including location and storm direction. Reliable estimation of design criteria requires incorporation of covariate effects within extreme value models. We present a spatiodirectional model for extreme waves in the Gulf of Mexico motivated by the nonhomogeneous Poisson model for peaks over threshold. The model is applied to storm peak significant wave height HS for arbitrary geographic areas from the proprietary Gulf of Mexico Oceanographic Study (GOMOS) hindcast for the US region of the Gulf of Mexico for the period of 1900–2005. At each location, directional variability is modeled using a nonparametric directional location and scale; data are standardized (or “whitened”) with respect to local directional location and scale to remove directional effects. For a suitable choice of threshold, the rate of occurrence of threshold exceedences of whitened storm peak HS with direction per location is modeled as a Poisson process. The size of threshold exceedences is modeled using a generalized Pareto form, the parameters of which vary smoothly in space, and are estimated within a roughness-penalized likelihood framework using natural thin plate spline forms in two spatial dimensions. By reparameterizing the generalized Pareto model in terms of asymptotically independent parameters, an efficient back-fitting algorithm to estimate the natural thin plate spline model is achieved. The algorithm is motivated in an appendix. Design criteria, estimated by simulation, are illustrated for a typical neighborhood of 17×17 grid locations. Applications to large areas consisting of more than 2500 grid locations are outlined.


2020 ◽  
Vol 8 (1) ◽  
pp. 157-171 ◽  
Author(s):  
Himchan Jeong ◽  
Emiliano A. Valdez

AbstractFor observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.


2018 ◽  
Vol 246 ◽  
pp. 01096
Author(s):  
Qiumei Ma ◽  
Lihua Xiong ◽  
Chong-Yu Xu ◽  
Shenglian Guo

Satellite precipitation estimates (SPE) product with high spatiotemporal resolution is a potential alternative to traditional ground-based gauge precipitation. However, SPE is frequently biased due to its indirect measurement, and thus bias correction is necessary before applying to a specific region. An improved distribution mapping method, i.e., Extended Mixture Distribution (EMD) of censored Gamma and generalized Pareto distributions, was established. The advantage of EMD method is that it describes both moderate and extreme values well and carries on the traditional censored, shifted Gamma distribution to combine the precipitation occurrence/non-occurrence events together. Then the EMD method was applied to the Integrated Multi-satellitE Retrievals for GPM product (IMERG) as statistical post-processing over Yangtze River basin. The Version-2 Gridded dataset of daily Surface Precipitation from China Meteorological Administration (GSP-CMA) was taken as reference. The adequacy of bias corrected IMERG precipitation was assessed and the results showed that (1) the Root Mean Squared Error and Relative Bias between bias-corrected IMERG precipitation and reference are significantly reduced relative to the raw IMERG estimates; (2) the performance of extreme values of IMERG in Yangtze River basin is enhanced since both the under- and over-estimation of the raw IMERG are compromised, due to the generalized Pareto distribution introduced in EMD which is enable to describe the extreme value distribution. This highlights the improved distribution mapping method, EMD is flexible and robust to bias correct the IMERG precipitation to obtain higher accuracy of SPE despite the coarse resolution of reference.


2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25


Author(s):  
Andrew Cornett

Many deck-on-pile structures are located in shallow water depths at elevations low enough to be inundated by large waves during intense storms or tsunami. Many researchers have studied wave-in-deck loads over the past decade using a variety of theoretical, experimental, and numerical methods. Wave-in-deck loads on various pile supported coastal structures such as jetties, piers, wharves and bridges have been studied by Tirindelli et al. (2003), Cuomo et al. (2007, 2009), Murali et al. (2009), and Meng et al. (2010). All these authors analyzed data from scale model tests to investigate the pressures and loads on beam and deck elements subject to wave impact under various conditions. Wavein- deck loads on fixed offshore structures have been studied by Murray et al. (1997), Finnigan et al. (1997), Bea et al. (1999, 2001), Baarholm et al. (2004, 2009), and Raaij et al. (2007). These authors have studied both simplified and realistic deck structures using a mixture of theoretical analysis and model tests. Other researchers, including Kendon et al. (2010), Schellin et al. (2009), Lande et al. (2011) and Wemmenhove et al. (2011) have demonstrated that various CFD methods can be used to simulate the interaction of extreme waves with both simple and more realistic deck structures, and predict wave-in-deck pressures and loads.


2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.


Sign in / Sign up

Export Citation Format

Share Document