# graphicalExtremes v0.1.0

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## Statistical Methodology for Graphical Extreme Value Models

Statistical methodology for sparse multivariate extreme value models. Methods are provided for exact simulation and statistical inference for multivariate Pareto distributions on graphical structures as described in the paper 'Graphical Models for Extremes' by Engelke and Hitz (2018) <arXiv:1812.01734>.

# graphicalExtremes

The goal of graphicalExtremes is to provide an implementation of the statistical methodology paper Engelke and Hitz (2019, JRSSB) for sparse multivariate extreme value models. This includes exact simulation algorithms and statistical inference methods for multivariate Pareto distributions on graphical structures.

## Installation

You can install the development version of graphicalExtremes from GitHub with:

# install.packages("devtools")
devtools::install_github("sebastian-engelke/graphicalExtremes")


## Functions in graphicalExtremes

 Name Description emp_chi Empirical estimation of extremal correlation $\chi$ rmpareto Sampling of a multivariate Pareto distribution rmpareto_tree Sampling of a multivariate Pareto distribution on a tree emp_chi_mat Empirical estimation of extremal correlation matrix $\chi$ dim_Gamma Is Gamma square matrix? Gamma2chi Transformation of the Huesler--Reiss variogram $\Gamma$ to extremal correlation $\chi$ simu_px_dirichlet Simulate Dirichlet extremal functions simu_px_HR Simulate HR extremal functions data2mpareto Data standardization to multivariate Pareto scale Gamma2Sigma Transformation of $\Gamma$ matrix to $\Sigma^{(k)}$ matrix mst_HR Fitting of Huesler--Reiss minimum spanning tree Gamma2chi_3D Compute theoretical $\chi$ in 3D simu_px_tree_HR Simulate HR extremal functions on a tree complete_Gamma Completion of Gamma matrix on block graphs chi2Gamma Transformation of extremal correlation $\chi$ to the Huesler--Reiss variogram $\Gamma$ fmpareto_HR Parameter fitting for multivariate Huesler--Reiss Pareto distribution Gamma2graph Transformation of $\Gamma$ matrix to graph object select_edges Select edges to add to a graph emp_vario Estimation of the variogram matrix $\Gamma$ of the Huesler--Reiss distribution simu_px_tree_dirichlet Simulate Dirichlet extremal functions on a tree logLH_HR Full censored log-likelihood of HR model Sigma2Gamma Transformation of $\Sigma^{(k)}$ matrix to $\Gamma$ matrix mparetomargins Marginalize multivariate Pareto dataset set_graph_parameters Set graphical parameters par2Gamma Create $\Gamma$ from vector fmpareto_graph_HR Parameter fitting for multivariate Huesler--Reiss Pareto distributions on block graphs graphicalExtremes graphicalExtremes: Statistical methodology for graphical extreme value models. logdV_HR Compute the exponent measure density of HR distribution logdVK_HR Compute censored exponent measure rmstable Sampling of a multivariate max-stable distribution simu_px_tree_logistic Simulate logistic extremal functions on a tree rmstable_tree Sampling of a multivariate max-stable distribution on a tree simu_px_logistic Simulate logistic extremal functions simu_px_neglogistic Simulate negative logistic extremal functions unif Uniform margin censor Censor dataset V_HR Compute exponent measure Gamma2par Extract upper triangular part of $\Gamma$ No Results!