mixbeta | R Documentation |
Calculate the mixed beta dependence model likelihood in conjunction with fbvpot.
mixbeta(w, p, ...) mixbetaLH(w, p, ...)
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. |
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.
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).
Eric Gilleland and Dan Cooley
Beirlant, J., Y. Goegebeur, J. Segers, and J. Teugels (2004). Statistics of Extremes: Theory and Applications. Wiley, West Sussex, England, United Kingdom, 490 pp.
fbvpot
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 )
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