PotFit {fExtremes} | R Documentation

## Modelling Peaks Over a Threshold

### Description

a collection and description of functions to model point processes over a threshold, POT, based on R's 'evir' package.

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

    potSim(x, threshold, nextremes = NA, run = NA)
    potFit(x, threshold = NA, nextremes = NA, run = NA, ...)

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

### Arguments

`doplot` | a logical. Should the results be plotted?
`nextremes` | the number of upper extremes to be used (either this or `threshold` must be given but not both).
`object` | [summary] - a fitted object of class `"potFit"`.
`run` | if the data are to be declustered the run length parameter for the runs method, see `deCluster`, should be entered here.
`threshold` | a threshold value, either `threshold` or `nextremes` must be given, but not both).
`which` | if `which` is set to `ask` the function will interactively ask which plot should be displayed. By default this value is set to `FALSE` and then those plots will be displayed for which the elements in the logical vector `which` ar set to `TRUE`; by default all four elements are set to `"all"`.
`x` | numeric vector of data, which may have a `times` attribute containing (in an object of class `"POSIXct"`, or an object that can be converted to that class; see `as.POSIXct`) the times/dates of each observation. If no `times` attribute exists, the data are assumed to be equally spaced. Note, the argument name is different for `potFit` and `pot`. [print][plot] - a fitted object of class `"potFit"`.
`...` | 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

Parameter Estimation:
`potFit` uses `optim` for point process likelihood maximization.

Methods:
The plot method `plot.pot` provides seven different plots for assessing fitted POT model. The user selects the plot type from a menu. Plot 1 displays the exceedance process of the chosen threshold. Plots 2-4 assess the Poisson nature of the exceedance process by looking at the scaled gaps between exceedances, which should be iid unit exponentially distributed. Plots 5-6 assess the GPD nature of the excesses by looking at suitably defined residuals, which should again be iid unit exponentially distributed. Option 8 allows the user to call GPD plotting functions. If plot 1 or 2 from the GPD plots is selected as the final plot (i.e. option 8 is selected, followed by option 1 or 2), a list object containing details of the plot is returned invisibly. This object should be used as the first argument of `gpdqPlot` or `gpdsfallPlot` to add quantile estimates or expected shortfall estimates to the plot.

### Value

Both, `potFit` and `pot` return an object of class `"pot"` describing the fit including parameter estimates and standard errors.

### Examples

    ## SOURCE("fExtremes.53C-PotFit")

    ## Use Danish Fire Insurance Loss Data:
       data(danish)

    ## Fit:
       xmpExtremes("\nStart: POT Parameter Estimate >")
       fit = potFit(danish, threshold = 10)
       print(fit)

    ## Summary with Diagnostic Plots:
       xmpExtremes("\nNext: Diagnostic Analysis >")
       par(mfrow = c(3, 3), cex = 0.5)
       summary(fit)

[Package fExtremes version 221.10065 Index]