fExtremes (version 220.10063)

PPFit: 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: 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

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

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)

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

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.

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).

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)