angdensity {extremis}

Empirical-Likelihood Based Inference for the Angular Density

Description

This function computes empirical-likelihood based estimators for the angular distribution function of a bivariate extreme value distribution.

Usage

angdensity(Y, tau = 0.95, nu, grid = seq(0.01, 0.99, length = 2^8),
	   method = "euclidean", raw = TRUE)

Arguments

Y

data frame with two columns from which the estimate is to be computed.

tau

value used to threshold the data; by default it is set as the 0.95 quantile of the pseudo-radius.

nu

concentration parameter of beta distribution which controls the amount of smoothing.

grid

grid with coordinates of the points where the angular density is estimated; by default grid = seq(0.01, 0.99, length = 2^8).

method

a character string setting the method to be used. By default method = "euclidean", the other option being method = "empirical". See details.

raw

logical; if TRUE, Y will be converted to unit Fréchet scale. If FALSE, Y will be understood as already in unit Fréchet scale.

Details

The smooth angular density was introduced in by de Carvalho et al (2013). method = "euclidean" implements the version of the method based on Euclidean likelihood weights, whereas method = "empirical" uses Empirical likelihood weights.

Value

h

the estimate angular density values.

grid

grid with coordinates of the points where the angular density is estimated.

w

pseudo-angles.

nu

concentration parameter of the Beta-kernel.

Y

raw data.

The plot method depicts the smooth angular density.

Author(s)

Miguel de Carvalho

References

de Carvalho, M., Oumow, B., Segers, J. and Warchol, M. (2013) A Euclidean likelihood estimator for bivariate tail dependence. Communications in Statistics—Theory and Methods, 42, 1176–1192.

Examples

## de Carvalho et al (2013, Fig. 7)
data(beatenberg)
attach(beatenberg)
fit <- angdensity(beatenberg, tau = 0.98, nu = 163, raw = FALSE)
plot(fit)
rug(fit$w)