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Bivariate generalized Pareto distribution in practice: models and estimation
Author(s) -
Rakonczai Pál,
Zempléni András
Publication year - 2012
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.1144
Subject(s) - bivariate analysis , generalized pareto distribution , pareto distribution , econometrics , mathematics , lomax distribution , estimation , pareto principle , statistics , distribution (mathematics) , economics , extreme value theory , mathematical analysis , management
There is often interest in understanding how the extremely high/low values of different processes are related to each other. One possible way to tackle this problem is via an asymptotic approach, which involves fitting the multivariate generalized Pareto distribution (MGPD) to data that exceed a suitably high threshold. There are two possible definitions of the MGPD. The first, which has classically been used, consider values that jointly exceed the thresholds for all components. The second definition considers those values that exceed a threshold for at least one component. The first definition is widely investigated. So, here, we focus on the second type of definition (MGPD type II). One aim of this paper is to investigate the applicability of classical parametric dependence models within the MGPD type II. Because the set of applicable asymmetric dependence models is more restricted in this framework, a general transformation is proposed for creating asymmetric models from the well‐known symmetric ones. We apply the proposed approach to the exceedances of bivariate wind speed data and outline methods for calculating prediction regions, as well as evaluating goodness‐of‐fit. Copyright © 2012 John Wiley & Sons, Ltd.