extRemes (version 2.1-3)

mixbeta: Mixed Beta Dependence Model Likelihood

Description

Calculate the mixed beta dependence model likelihood in conjunction with fbvpot.

Usage

mixbeta(w, p, ...)
mixbetaLH(w, p, ...)

Value

mixbeta returns a vector giving the likelihood contribution for each angular component value and mixbetaLH calls mixbeta 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

numeric of length 4 giving the values of the logistic dependence model parameter.

...

Not used.

Author

Eric Gilleland and Dan Cooley

Details

The mixed beta dependence model is given by

p1 * dbeta( w, shape1 = nu1 * pi1, shape2 = nu1 * ( 1 - pi1 ) ) + ( 1 - p1 ) * dbeta( w, shape1 = nu2 * pi2, shape2 = nu2 * ( 1 - pi2 ) )

where nu1 = p[ 1 ], nu2 = p[ 2 ], pi1 = p[ 3 ], p1 = p[ 4 ], and pi2 = ( 1/2 - p[ 4 ] * p[ 3 ] ) / ( 1 - p[ 4 ] ). 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.

See Also

fbvpot

Examples

data( "SantaAna" )

Z <- SantaAna[,3:4]

mfit1 <- fevd( x = temp, data = Z, threshold = 36.75, type = "GP" )
mfit2 <- fevd( x = windspeeds, data = Z, threshold = 7.09875, type = "GP" )

fit2 <- fbvpot( x = Z, threshold = apply( Z, 2, quantile, probs = 0.95 ),
	       dep.model = "mixbeta", init = c( 1, 2, 0.5, 0.5 ),
	       tform = "tf", fit = list( mfit1, mfit2 ) )
fit2

plot( fit2 )

hist( fit2 )