fExtremes (version 220.10063)

PotFit: 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: ll{ 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, \dots)
## S3 method for class 'potFit':
plot(x, which = "all", \dots)
## S3 method for class 'potFit':
summary(object, doplot = TRUE, which  = "all", \dots)

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 elemen

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

...

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.

Value

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

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.

Examples

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

## Use Danish Fire Insurance Loss Data:
   data(danish)
   
## Fit:
   xmpExtremes("Start: POT Parameter Estimate >")
   fit = potFit(danish, threshold = 10)  
   print(fit)
   
## Summary with Diagnostic Plots:
   xmpExtremes("Next: Diagnostic Analysis >")
   par(mfrow = c(3, 3), cex = 0.5)
   summary(fit)