fExtremes (version 251.70)

PotModelling: 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 POT object, summary summary method for a fitted POT object, gevrlevelPlot k-block return level with confidence intervals. }

Usage

potSim(x, u = quantile(x, 0.95), run = 1)
potFit(x, u = quantile(x, 0.95), run = 1, title = NULL, description = NULL) 
show.fPOTFIT(object)
## S3 method for class 'fPOTFIT':
plot(x, which = "ask", \dots)
## S3 method for class 'fPOTFIT':
summary(object, doplot = TRUE, which  = "all", \dots)

Arguments

description

a character string which allows for a brief description.

doplot

a logical. Should the results be plotted?

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.

title

a character string which allows for a project title.

u

a threshold value.

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

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

• The function potFit returns an object of class "fPOTFIT" describing the fit including parameter estimates and standard errors.

Details

Parameter Estimation: potFit uses the optimization function optim for point process likelihood maximization to estimate the parameters. Methods: The plot method plot provides seven different plots for assessing fitted POT models. 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

## Use Danish Fire Insurance Loss Data:
   x = as.timeSeries(data(danishClaims))
   
## potFit - 
   # Fit Parameters:
   fit = potFit(x, u = 10)  
   print(fit)
   
## summary -
   # Summary with Diagnostic Plots:
   par(mfrow = c(3, 3), cex = 0.5)
   summary(fit)