fitpp {POT}

Fitting the point process characterisation to exceedances above a threshold

Description

This function estimates the point process characterisation from exceedances above a threshold.

Usage

fitpp(data, threshold, noy = length(data) / 365.25, start, ...,
std.err.type = "observed", corr = FALSE, method = "BFGS", warn.inf = TRUE)

Arguments

data

A numeric vector.

threshold

A numeric value giving the threshold for the GPD.

noy

Numeric. The number of year of observation.

start

A named list that gives the starting values for the optimization routine. Each list argument must correspond to one parameter to be estimated. May be missing.

...

Other optional arguments to be passed to the optim function, allow hand fixed parameters (only - see the Note section.

std.err.type

A character string. If "observed", the standard errors are derived from the observed Fisher information matrix. If "none", standard errors are not computed.

corr

Logical. Does the asymptotic correlation matrix has to be computed? Default is "not computed" - e.g. FALSE.

method

A character string specifying which numerical optimization procedure has to be used. See optim for more details.

warn.inf

Logical. If TRUE (default), users will be warned if the log-likelihood is not finite at starting values - as it may cause some problem during the optimation stage.

Value

This function returns a list with components:

fitted.values

A vector containing the estimated parameters.

std.err

A vector containing the standard errors.

fixed

A vector containing the parameters of the model that have been held fixed.

param

A vector containing all parameters (optimized and fixed).

deviance

The deviance at the maximum likelihood estimates.

corr

The correlation matrix.

convergence, counts, message

Components taken from the list returned by optim - for the mle method.

threshold

The threshold passed to argument threshold.

nat, pat

The number and proportion of exceedances.

data

The data passed to the argument data.

exceed

The exceedances, or the maxima of the clusters of exceedances.

scale

The scale parameter for the fitted generalized Pareto distribution.

std.err.type

The standard error type - for 'mle' only. That is Observed Information matrix of Fisher.

var.thresh

Logical. Specify if the threshold is a varying one - 'mle' only. For other methods, threshold is always constant i.e. var.thresh = FALSE. Not implemented yet.

Author(s)

Mathieu Ribatet

References

Coles, S. (2001) An Introduction to Statistical Modelling of Extreme Values. Springer Series in Statistics. London.

Embrechts, P and Kluppelberg, C. and Mikosch, T (1997) Modelling Extremal Events for Insurance and Finance. Springers.

Pickands, J. (1975) Statistical Inference Using Extreme Order Statistics. Annals of Statistics. 3:119–131.

Examples

x <- rgpd(1000, 0, 1, 0.2)
fitpp(x, 0)