angextrapo {mev}R Documentation

Bivariate angular dependence function for extrapolation based on rays

Description

The scale parameter g(w)g(w) in the Ledford and Tawn approach is estimated empirically for xx large as

Pr(XP>xw,YP>x(1w))Pr(XP>x,YP>x)\frac{\Pr(X_P>xw, Y_P>x(1-w))}{\Pr(X_P>x, Y_P>x)}

where the sample (XP,YPX_P, Y_P) are observations on a common unit Pareto scale. The coefficient η\eta is estimated using maximum likelihood as the shape parameter of a generalized Pareto distribution on min(XP,YP)\min(X_P, Y_P).

Usage

angextrapo(dat, qu = 0.95, w = seq(0.05, 0.95, length = 20))

Arguments

dat

an nn by 22 matrix of multivariate observations

qu

quantile level on uniform scale at which to threshold data. Default to 0.95

w

vector of unique angles between 0 and 1 at which to evaluate scale empirically.

Value

a list with elements

References

Ledford, A.W. and J. A. Tawn (1996), Statistics for near independence in multivariate extreme values. Biometrika, 83(1), 169–187.

Examples

angextrapo(rmev(n = 1000, model = 'log', d = 2, param = 0.5))

[Package mev version 1.17 Index]