extRemes (version 2.1-3)

logistic: Logistic Dependence Model Likelihood

Description

Calculate the logistic dependence model (negative log) likelihood.

Usage

logistic(w, p, ...)
logisticLH( w, p, ... )

Value

logistic returns a vector giving the likelihood contribution for each angular component value and logisticLH calls logistic and returns the negative of the sum of the log of these values (i.e., the negative log-likelihood).

Arguments

w

numeric vector giving the angular component of the bivariate data.

p

single numeric giving the value of the logistic dependence model parameter.

...

Not used.

Author

Eric Gilleland and Dan Cooley

Details

This function is used by the fbvpot function to fit a bivariate POT model using the logistic dependence model. The logistic dependence model has a single parameter, and is given by (Eq (8.11) in Coles 2001)

0.5 * ( p^(-1) - 1 ) * ( ( w * (1 - w) )^(-1 - p^(-1) ) ) * ( ( w^ (-1 / p) + ( 1 - w )^( -1 / p ) )^( p - 2 ) )

See Beirlant et al. (2004) for a thorough treatment of multivariate extreme-value analysis.

References

Beirlant, J., Y. Goegebeur, J. Segers, and J. Teugels (2004). Statistics of Extremes: Theory and Applications. Wiley, West Sussex, England, United Kingdom, 490 pp.

Coles, S. G. (2001). An introduction to statistical modeling of extreme values, London: Springer-Verlag, 208 pp.

See Also

fbvpot

Examples

# See the help file for 'fbvpot' for an example (the logistic dependence model is the default).