fitpp {POT} | R Documentation

## 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)

[Package POT version 1.1-7 Index]