fitbvgpd  R Documentation 
Fitting a bivariate extreme value distribution to bivariate exceedances over thresholds using censored maximum likelihood procedure.
fitbvgpd(data, threshold, model = "log", start, ..., cscale = FALSE, cshape = FALSE, std.err.type = "observed", corr = FALSE, warn.inf = TRUE, method = "BFGS")
data 
A matrix with two columns which gives the observation
vector for margin 1 and 2 respectively. 
threshold 
A numeric vector for the threshold (of length 2). 
model 
A character string which specifies the model used. Must
be one of 
start 
Optional. A list for starting values in the fitting procedure. 
... 
Additional parameters to be passed to the

cscale 
Logical. Should the two scale parameters be equal? 
cshape 
Logical. Should the two shape parameters be equal? 
std.err.type 
The type of the standard error. Currently, one
must specify 
corr 
Logical. Should the correlation matrix be computed? 
warn.inf 
Logical. Should users be warned if likelihood is not finite at starting values? 
method 
The optimization method, see 
The bivariate exceedances are fitted using censored likelihood procedure. This methodology is fully described in Ledford (1996).
Most of models are described in Kluppelberg (2006).
The function returns an object of class c("bvpot","pot")
. As
usual, one can extract several features using fitted
(or
fitted.values
), deviance
,
logLik
and AIC
functions.
fitted.values 
The maximum likelihood estimates of the bivariate extreme value distribution. 
std.err 
A vector containing the standard errors  only present when the observed information matrix is not singular. 
var.cov 
The asymptotic variance covariance matrix  only presents when the observed information matrix is not singular. 
deviance 
The deviance. 
corr 
The correlation matrix. 
convergence, counts, message 
Informations taken from the

threshold 
The marginal thresholds. 
pat 
The marginal proportion above the threshold. 
nat 
The marginal number above the threshold. 
data 
The bivariate matrix of observations. 
exceed1, exceed2 
The marginal exceedances. 
call 
The call of the current function. 
model 
The model for the bivariate extreme value distribution. 
chi 
The chi statistic of Coles (1999). A value near 1 (resp. 0) indicates perfect dependence (resp. independence). 
Because of numerical problems, their exists artificial numerical constraints imposed on each model. These are:
For the logistic and asymmetric logistic models: alpha must lie in [0.05, 1] instead of [0,1];
For the negative logistic model: alpha must lie in [0.01, 15] instead of [0, infinity[;
For the asymmetric negative logistic model: alpha must lie in [0.2, 15] instead of [0, infinity[;
For the mixed and asymmetric mixed models: None artificial numerical constraints are imposed.
For this purpose, users must check if estimates are near these artificial numerical constraints. Such cases may lead to substantial biases on the GP parameter estimates. One way to detect quickly if estimates are near the border constraints is to look at the standard errors for the dependence parameters. Small values (i.e. < 1e5) often indicates that numerical constraints have been reached.
In addition, users must be aware that the mixed and asymmetric mixed models can not deal with perfect dependence.
Thus, user may want to plot the Pickands' dependence function to see
if variable are near independence or dependence cases using the
pickdep
function.
Mathieu Ribatet
Coles, S., Heffernan, J. and Tawn, J. (1999) Dependence Measure for Extreme Value Analyses. Extremes, 2:4 339–365.
Kl\"uppelberg, C., and May A. (2006) Bivariate extreme value distributions based on polynomial dependence functions. Mathematical Methods in the Applied Sciences, 29: 1467–1480.
Ledford A., and Tawn, J. (1996) Statistics for near Independence in Multivariate Extreme Values. Biometrika, 83: 169–187.
The following usual generic functions are available
print
,
plot
and
anova
as well as new generic functions
retlev
and
convassess
.
See also pickdep
, specdens
.
For optimization in R, see optim
.
x < rgpd(1000, 0, 1, 0.25) y < rgpd(1000, 3, 1, 0.25) ind < fitbvgpd(cbind(x, y), c(0, 3), "log") ind ind2 < fitbvgpd(cbind(x, y), c(0, 3), "log", alpha = 1) ind2 ind3 < fitbvgpd(cbind(x, y), c(0, 3), cscale = TRUE) ind3 ##The mixed model can not deal with perfect dependent variables ##Thus, there is a substantial bias in GPD parameter estimates dep < fitbvgpd(cbind(x, x + 3), c(0, 3), "mix") dep
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