angextrapo {mev}

Bivariate angular dependence function for extrapolation based on rays

Description

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

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

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

Usage

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

Arguments

dat

an n by 2 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

• w: angles between zero and one

• g: scale function at a given value of w

• eta: Ledford and Tawn tail dependence coefficient

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))