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Maximum likelihood estimation of the point process of extremes

Source: R/mle.R
fit.pp.Rd

Data above threshold is modelled using the limiting point process of extremes.

Usage

fit.pp(
  xdat,
  threshold = 0,
  npp = 1,
  np = NULL,
  method = c("nlminb", "BFGS"),
  start = NULL,
  show = FALSE,
  fpar = NULL,
  warnSE = FALSE
)

Arguments

xdat

a numeric vector of data to be fitted.

threshold

the chosen threshold.

npp

number of observation per period. See Details

np

number of periods of data, if xdat only contains exceedances.

method

the method to be used. See Details. Can be abbreviated.

start

named list of starting values

show

logical; if TRUE (the default), print details of the fit.

fpar

a named list with optional fixed components loc, scale and shape

warnSE

logical; if TRUE, a warning is printed if the standard errors cannot be returned from the observed information matrix when the shape is less than -0.5.

Value

a list containing the following components:

  • estimate a vector containing all parameters (optimized and fixed).

  • std.err a vector containing the standard errors.

  • vcov the variance covariance matrix, obtained as the numerical inverse of the observed information matrix.

  • threshold the threshold.

  • method the method used to fit the parameter. See details.

  • nllh the negative log-likelihood evaluated at the parameter estimate.

  • nat number of points lying above the threshold.

  • pat proportion of points lying above the threshold.

  • convergence components taken from the list returned by optim. Values other than 0 indicate that the algorithm likely did not converge (in particular 1 and 50).

  • counts components taken from the list returned by optim.

Details

The parameter npp controls the frequency of observations. If data are recorded on a daily basis, using a value of npp = 365.25 yields location and scale parameters that correspond to those of the generalized extreme value distribution fitted to block maxima.

References

Coles, S. (2001), An introduction to statistical modelling of extreme values. Springer : London, 208p.

Examples

data(eskrain)
pp_mle <- fit.pp(eskrain, threshold = 30, np = 6201)
plot(pp_mle)