gpdbiv: Implements Bivariate POT Method
In evir: Extreme Values in R

Description Usage Arguments Details Value References See Also Examples

Returns an object of class "gpdbiv" representing the fit of a bivariate POT (peaks over thresholds) model for joint excesses over thresholds.

1 2	gpdbiv(data1 = NA, data2 = NA, u1 = NA, u2 = NA, ne1 = NA, ne2 = NA, global = FALSE, method = "BFGS", ...)

`data1`	first data vector
`data2`	second data vector
`u1`	threshold for `data1` (either this or `ne1` must be given but not both)
`u2`	threshold for `data2` (either this or `ne2` must be given but not both)
`ne1`	number of upper extremes to be used for `data1` (either this or `u1` must be given but not both)
`ne2`	number of upper extremes to be used for `data2` (either this or `u2` must be given but not both)
`global`	should a global maximisation of the likelihood with respect to marginal and dependence parameters be undertaken. The default alternative is a two-stage local fit where first the marginal parameters are estimated and then the dependence parameter. This is much faster than a global fit.
`method`	the optimization method (see `optim`). The argument has been created (as distinct from ...) in order to make the `"BFGS"` method the default, as the default used by `optim` is not recommended for the one-dimensional optimizations that occur when `global = FALSE`.
`...`	other arguments passed to `optim`

This function implements a model suggested by Richard Smith (see references below). The marginal excess distributions are GPD distributions, as suggested by univariate EVT and implemented in gpd. The dependence specification is known as the logistic or Gumbel dependence structure, but it would be easy to program alternatives.

An object of class "gpdbiv" representing the fit and including parameter estimates and standard errors.

Multivariate Threshold Methods, Richard L. Smith, in Extreme Value Theory and Applications, ed. J. Galambos, published by Kluwer, pages 225-248, 1994.

Markov Chain Models for Threshold Exceedances, R.L. Smith, J.A. Tawn, S.G. Coles, Biometrika 84, 249-268, 1997.

gpd, plot.gpdbiv, interpret.gpdbiv

data(bmw) ; data(siemens)
out <- gpdbiv(-bmw, -siemens, ne1 = 100, ne2 = 100)
interpret.gpdbiv(out, 0.05, 0.05)
## Not run: plot(out)

Thresholds: 0.0342151 0.02688724 
Extreme levels of interest (x,y): 0.05 0.05 
P(X exceeds x) 0.005060484 
P(Y exceeds y) 0.00213182 
P(X exceeds x AND Y exceeds y) 0.001316135 
P(X exceeds x) * P(Y exceeds y) 1.078804e-05 
P(Y exceeds y GIVEN X exceeds x) 0.2600809 
P(X exceeds x GIVEN Y exceeds y) 0.6173763