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graphicalExtremes (version 0.2.0)

Statistical Methodology for Graphical Extreme Value Models

Description

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 (2020) .

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install.packages('graphicalExtremes')

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605

Version

0.2.0

License

GPL-3

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Repository

https://github.com/sebastian-engelke/graphicalExtremes

Maintainer

Sebastian Engelke

Last Published

December 2nd, 2022

Functions in graphicalExtremes (0.2.0)

Transformation of extremal correlation \(\chi\) to the Huesler--Reiss variogram \(\Gamma\)

complete_Gamma_general_demo

DEMO-VERSION: Completion of non-decomposable Gamma matrices

complete_Gamma_general_split

Non-decomposable completion of variogram matrices

complete_Gamma_decomposable

Completion of decomposable Gamma matrices

check_Gamma_and_graph

Check input graph and Gamma matrix

check_split_by_sep

Identify pairs of vertices that are split by a separator

Check input graph

Completion of Gamma matrices

complete_Gamma_general

Non-decomposable completion of variogram matrices

Empirical estimation of extremal correlation matrix \(\chi\)

Estimation of the variogram matrix \(\Gamma\) of a Huesler--Reiss distribution

complete_Gamma_one_step

Completion of two-clique decomposable Gamma matrices

Upper Danube basin dataset

emp_chi_multdim

Empirical estimation of extremal correlation \(\chi\)

Data standardization to multivariate Pareto scale

Learning extremal graph structure

Is Gamma square matrix?

Helper function to compute the axis limits of a plot with given x, y data and optionally a fixed x-y-ratio and correcting the latitude/longitude scale at different latitudes

Fit value(s) in interval

fillFixedParams

Helper function to combine par with fixed params (in init)

Fitting extremal minimum spanning tree

Find a separator set for two vertices

flightCountMatrixToConnectionList

Convert flight counts to connection list

fit_graph_to_Theta

Experimental: Fit graph using empirical Theta matrix

Flights delay data

graphicalExtremes

graphicalExtremes: Statistical methodology for graphical extreme value models.

fmpareto_HR_MLE

Parameter fitting for multivariate Huesler--Reiss Pareto distribution

fmpareto_graph_HR

Parameter fitting for Huesler--Reiss graphical models

generate_random_tree

Generate a random tree

getSubMatrixForSubgraph

Get the submatrix corresponding to a subgraph

Create a list of separators

Compute Huesler--Reiss log-likelihood, AIC, and BIC

Marginalize multivariate Pareto dataset

Compute the exponent measure density of HR distribution

generate_random_spd_matrix

Generate a random symmetric positive definite matrix

generate_random_model

Generate random Huesler--Reiss Models

Number of cores to be used in parallel computations

generate_random_connected_graph

Generate a random connected graph

Tolerances to be used in computations

generate_random_chordal_graph

Generate a random chordal graph

simu_px_tree_logistic

Simulate logistic extremal functions on a tree

simu_px_tree_dirichlet

Simulate Dirichlet extremal functions on a tree

generate_random_Gamma

Generate a random Gamma matrix

Sampling of a multivariate Pareto distribution

Plot flight data

Split graph into invariant subgraphs

generate_random_graphical_Gamma

Generate a random Gamma matrix for a given graph

simu_px_logistic

Simulate logistic extremal functions

simu_px_dirichlet

Simulate Dirichlet extremal functions

Sampling of a multivariate Pareto distribution on a tree

Compute censored exponent measure

generate_random_cactus

Generate a random cactus graph

Performs Gaussian likelihood optimization under Laplacian matrix constraints.

Sampling of a multivariate max-stable distribution

Fast computation of diag(y %% M %% t(y))

Simulate HR extremal functions

Full censored log-likelihood of HR model

simu_px_neglogistic

Simulate negative logistic extremal functions

simu_px_tree_HR

Simulate HR extremal functions on a tree

generate_random_integer_Gamma

Generate a random Gamma matrix containing only integers

Sampling of a multivariate max-stable distribution on a tree

get_cliques_and_separators_OLD

Get Cliques and Separators of a graph

parToMatricesFactory

Factory: parToMatrices

Create Gamma or Theta from vector

partialMatrixToGraph

Transformation of a partial matrix to a graph

get_cliques_and_separators

Get Cliques and Separators of a graph

Transformation of \(\Sigma\) and \(\Sigma^k\) matrix to \(\Gamma\) matrix

Transformation of matrix to graph object

Extract upper triangular part of \(\Gamma\)

Transformation of \(\Gamma\) matrix to \(\Sigma\) or \(\Sigma^k\) matrix

Transformation of \(\Gamma\) matrix to \(\Theta\) matrix

Computes the Z-matrix

Transformation of the Huesler--Reiss variogram \(\Gamma\) to extremal correlation \(\chi\)

Transformation of \(\Gamma\) matrix to \(\Theta\) matrix

Compute theoretical \(\chi\) in 3D

Compute exponent measure