Journal ArticleDOI
A Dynamic Mixture Model for Unsupervised Tail Estimation without Threshold Selection
TLDR
A new dynamically weighted mixture model, where one term of the mixture is the GPD, and the other is a light-tailed density distribution, which can be useful in unsupervised tail estimation, especially in heavy tailed situations and for small percentiles.Abstract:
Exceedances over high thresholds are often modeled by fitting a generalized Pareto distribution (GPD) on R+. It is difficult to select the threshold, above which the GPD assumption is enough solid and enough data is available for inference. We suggest a new dynamically weighted mixture model, where one term of the mixture is the GPD, and the other is a light-tailed density distribution. The weight function varies on R+ in such a way that for large values the GPD component is predominant and thus takes the role of threshold selection. The full data set is used for inference on the parameters present in the two component distributions and in the weight function. Maximum likelihood provides estimates with approximate standard deviations. Our approach has been successfully applied to simulated data and to the (previously studied) Danish fire loss data set. We compare the new dynamic mixture method to Dupuis' robust thresholding approach in peaks-over-threshold inference. We discuss robustness with respect to the choice of the light-tailed component and the form of the weight function. We present encouraging simulation results that indicate that the new approach can be useful in unsupervised tail estimation, especially in heavy tailed situations and for small percentiles.read more
Citations
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Journal ArticleDOI
Precipitation downscaling under climate change: Recent developments to bridge the gap between dynamical models and the end user
Douglas Maraun,Douglas Maraun,Fredrik Wetterhall,Andrew Ireson,Richard E. Chandler,Elizabeth J. Kendon,Martin Widmann,S. Brienen,S. Brienen,Henning W. Rust,Tobias Sauter,M. Themeßl,Victor Venema,Kwok Pan Chun,Clare Goodess,Richard G. Jones,Christian Onof,Mathieu Vrac,I. Thiele-Eich +18 more
TL;DR: In this paper, the authors integrate perspectives from meteorologists, climatologists, statisticians, and hydrologists to identify generic end user (in particular, impact modeler) needs and to discuss downscaling capabilities and gaps.
Journal ArticleDOI
Bayesian analysis of extreme events with threshold estimation
TL;DR: A mixture model is introduced that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold included.
Journal ArticleDOI
Stochastic downscaling of precipitation: From dry events to heavy rainfalls
M. Vrac,M. Vrac,Philippe Naveau +2 more
TL;DR: In this paper, the authors proposed a new distribution for local precipitation via a probability mixture model of Gamma and Generalized Pareto (GP) distributions, which was tested on real and simulated data, and also compared to classical rainfall densities.
Journal ArticleDOI
Extreme events: dynamics, statistics and prediction
Michael Ghil,Michael Ghil,Pascal Yiou,Stephane Hallegatte,Bruce D. Malamud,Philippe Naveau,A. Soloviev,Petra Friederichs,Vladimir Keilis-Borok,Dmitri Kondrashov,Vladimir Kossobokov,Olivier Mestre,C. Nicolis,Henning W. Rust,Peter Shebalin,Mathieu Vrac,Annette Witt,Annette Witt,Ilya Zaliapin +18 more
TL;DR: Two important results refer to the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum and the need for coupled modeling of natural and socio-economic systems.
Journal ArticleDOI
Parameter estimation of the generalized Pareto distribution—Part II
P. de Zea Bermudez,Samuel Kotz +1 more
TL;DR: In this article, the generalized Pareto distribution (GPD) has been widely used in the extreme value framework and several methods exist in the literature for estimating the GPD parameters.
References
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BookDOI
Markov Chain Monte Carlo in Practice
TL;DR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.
Book
Monte Carlo Statistical Methods
TL;DR: This new edition contains five completely new chapters covering new developments and has sold 4300 copies worldwide of the first edition (1999).
Journal ArticleDOI
Statistical Inference Using Extreme Order Statistics
TL;DR: In this article, a method for making statistical inferences about the upper tail of a distribution function is presented for estimating the probabilities of future extremely large observations, where the underlying distribution function satisfies a condition which holds for all common continuous distribution functions.