Description Usage Arguments Details Value Author(s) References See Also Examples
Fit multiple independent generalized Pareto models as the first step of conditional multivariate extreme values modelling following the approach of Heffernan and Tawn, 2004.
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data 
A matrix or data.frame, each column of which is to be modelled. 
mth 
Thresholds above which to fit the models. Only one of

mqu 
Quantiles above which to fit the models. Only one of

penalty 
How the likelihood should be penalized. Defaults to
'gaussian'. See documentation for 
maxit 
The maximum number of iterations to be used by the optimizer. 
trace 
Whether or not to tell the user how the optimizer is getting on. The argument is passed into 
verbose 
Controls whether or not the function print to screen every time it fits a model. Defaults to FALSE. 
priorParameters 
Only used if

x 
Object of class 
main 
Character vector of length four: titles for plots produced by 
xlab 
As 
nsim 
Number of simulations on which to base tolerance envelopes in 
alpha 
Significance level for tolerance and confidence intervals in 
... 
Further arguments to be passed to methods. 
The parameters in the generalized Pareto distribution are estimated for each column of the data in turn, independently of all other columns. Note, covariate modelling of GPD parameters is not supported.
Maximum likelihood estimation often fails with generalized Pareto distributions because of the likelihood becoming flat (see, for example, Hosking et al, 1985). Therefore the function allows penalized likelihood estimation, which is the same as maximum a posteriori estimation from a Bayesian point of view.
By default quadratic penalization is used, corresponding to using a Gaussian prior. If no genuine prior information is available, the following argument can be used. If xi = 1, the generalized Pareto distribution corresponds to the uniform distribution, and if xi is 1 or greater, the expectation is infinite. Thefore, xi is likely to fall in the region (1, 1). A Gaussian distribution centred at zero and with standard deviation 0.5 will have little mass outside of (1, 1) and so will often be a reasonable prior for xi. For log(sigma) a Gaussian distribution, centred at zero and with standard deviation 100 will often be vague. If a Gaussian penalty is specified but no parameters are given, the function will assume such indpendent priors.
Note that internally the function works with log(sigma), not sigma. The reasons are that quadratic penalization makes more sense for log(sigma) than for sigma (because the distribution of log(sigma) will be more nearly symmetric), and because it was found to stabilize computations.
The associated coef
, print
and summary
functions exponentiate the log(sigma) parameter to return results
on the expected scale. If you are accessesing the parameters
directly, however, take care to be sure what scale the results
are on.
Threshold selection can be carried out with the help of functions mrlPlot
and gpdRangeFit
.
An object of class 'migpd'. There are coefficients
, print
, plot
and summary
functions available.
Harry Southworth
J. E. Heffernan and J. A. Tawn, A conditional approach for multivariate extreme values, Journal of the Royal Statistical society B, 66, 497 – 546, 2004
J. R. M. Hosking and J. R. Wallis, Parameter and quantile estimation for the genralized Pareto distribution, Technometrics, 29, 339 – 349, 1987
mex
, mexDependence
, bootmex
,
predict.mex
, gpdRangeFit
, mrlPlot
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