R: Mixed Beta Dependence Model Likelihood

mixbeta {extRemes} | R Documentation

## Mixed Beta Dependence Model Likelihood

### Description

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

### Usage

    mixbeta(w, p, ...)

    mixbetaLH(w, p, ...)

### 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.

### 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.

### 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).

### Author(s)

Eric Gilleland and Dan Cooley

### 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 )

[Package extRemes version 2.0-12 Index]