PPFit {fExtremes} | R Documentation

## Modelling Point Processes

### Description

A collection and description of functions to model point processes, PP, over a threshold, based on R's 'ismev' package. The parameter estimation allows to include generalized linear modelling, GLM, of each parameter.

The functions are:

`potSim` | generates data from a point process,
`potFit` | fits empirical or simulated data to a point process,
`print` | print method for a fitted POT object of class ...,
`plot` | plot method for a fitted GEV object,
`summary` | summary method for a fitted GEV object,
`gevrlevelPlot` | k-block return level with confidence intervals.

### Usage

    ppFit(x, threshold, npy = 365, y = NULL, mul = NULL, sigl = NULL,
        shl = NULL, mulink = identity, siglink = identity, shlink =
        identity, method = "Nelder-Mead", maxit = 10000, ...)

    ## S3 method for class 'ppFit':
    print(x, ...)
    ## S3 method for class 'ppFit':
    plot(x, which = "ask", ...)
    ## S3 method for class 'ppFit':
    summary(object, doplot = TRUE, which = "all", ...)

### Arguments

`doplot` | a logical. Should the results be plotted?
`maxit` | [ppFit] - the maximum number of iterations.
`method` | [ppFit] - The optimization method (see `optim` for details).
`mul, sigl, shl` | [ppFit] - numeric vectors of integers, giving the columns of `ydat` that contain covariates for generalized linear modelling of the location, scale and shape parameters repectively (or `NULL` (the default) if the corresponding parameter is stationary).
`mulink, siglink, shlink` | [ppFit] - inverse link functions for generalized linear modelling of the location, scale and shape parameters repectively.
`npy` | [ppFit] - the number of observations per year/block.
`object` | [summary] - a fitted object of class `"ppFit"`.
`threshold` | [ppFit] - the threshold; a single number or a numeric vector of the same length as `x`.
`which` | [print][plot][summary] - a logical for each plot, denoting which plots should be created.
`x` | [ppFit] - a numeric vector of data to be fitted. [print][plot] - a fitted object of class `"ppFit"`.
`y` | [ppFit] - a matrix of covariates for generalized linear modelling of the parameters (or `NULL` (the default) for stationary fitting). The number of rows should be the same as the length of `x`.
`...` | [ppFit] - control parameters and plot parameters optionally passed to the optimization and/or plot function. Parameters for the optimization function are passed to components of the `control` argument of `optim`.

### Details

For non-stationary fitting it is recommended that the covariates within the generalized linear models are (at least approximately) centered and scaled (i.e. the columns of `ydat` should be approximately centered and scaled).

### Value

A list containing the following components. A subset of these components are printed after the fit. If `show` is `TRUE`, then assuming that successful convergence is indicated, the components `nexc`, `nllh`, `mle` and `se` are always printed.

`trans` | An logical indicator for a non-stationary fit.
`model` | A list with components `mul`, `sigl` and `shl`.
`link` | A character vector giving inverse link functions.
`threshold` | The threshold, or vector of thresholds.
`npy` | The number of observations per year/block.
`nexc` | The number of data points above the threshold.
`data` | The data that lie above the threshold. For non-stationary models, the data is standardized.
`conv` | The convergence code, taken from the list returned by `optim`. A zero indicates successful convergence.
`nllh` | The negative logarithm of the likelihood evaluated at the maximum likelihood estimates.
`vals` | A matrix with four columns containing the maximum likelihood estimates of the location, scale and shape parameters, and the threshold, at each data point.
`gpd` | A matrix with three rows containing the maximum likelihood estimates of corresponding GPD location, scale and shape parameters at each data point.
`mle` | A vector containing the maximum likelihood estimates.
`cov` | The covariance matrix.
`se` | A vector containing the standard errors.

For stationary models two plots are produced; a probability plot and a quantile plot. For non-stationary models two plots are produced; a residual probability plot and a residual quantile plot.

### Author(s)

Alec Stephenson for the code implemented from R's ismev package,
Stuart Scott for the original code, and Diethelm Wuertz for this R-port.

### References

Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer.

### Examples

    ## SOURCE("fExtremes.54C-PPFit")

    ## Use Rain Data:
       data(rain)

    ## Fit Point Process Model:
       xmpExtremes("Start: Parameter Fit for Point Process > ")
       fit = ppFit(x = rain[1:200], threshold = 10)
       print(fit)

    ## Summarize Results:
       xmpExtremes("Next: Diagnostic Analysis > ")
       par(mfrow = c(2, 2), cex = 0.75)
       summary(fit)
       xmpExtremes("Next: Interactive Plot > ")

    ## Interactive Plot:
       ##> par(mfrow = c(2, 2), cex = 0.75)
       ##> plot(fit)

[Package fExtremes version 221.10065 Index]