Fit multiple independent generalized Pareto models as the first step of conditional multivariate extreme values modelling following the approach of Heffernan and Tawn, 2004.
1 2 3 4 5 6 7 8 9 10 11 12  ## S3 method for class 'migpd'
ggplot(data, mapping = NULL, main = c("Probability plot",
"Quantile plot", "Return level plot", "Histogram and density"),
xlab = rep(NULL, 4), nsim = 1000, alpha = 0.05, ..., environment)
migpd(data, mth, mqu, penalty = "gaussian", maxit = 10000, trace = 0,
verbose = FALSE, priorParameters = NULL)
## S3 method for class 'migpd'
plot(x, main = c("Probability plot", "Quantile plot",
"Return level plot", "Histogram and density"), xlab = rep(NULL, 4),
nsim = 1000, alpha = 0.05, ...)

data 
A matrix or data.frame, each column of which is to be modelled. 
mapping, environment 
Further arguments to ggplot method. 
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. 
mth 
Marginal thresholds. Thresholds above which to fit the models.
Only one of 
mqu 
Marginal quantiles. 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 prints to screen every time it fits a model. Defaults to FALSE. 
priorParameters 
Only used if 
x 
Object of class 
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 phi=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
mrl
and gpdRangeFit
.
An object of class "migpd". There are coef
, print
,
plot
, ggplot
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
,
mrl
1 2 3 4 5 
Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
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