gevd.fit: Maximum Likelihood Fitting for the GEV distribution

In ilapros/ilaprosUtils: A Miscellaneous Collection of Functions I Tend to Use

Maximum Likelihood Fitting for the GEV distribution

Description

Maximum-likelihood fitting for the generalized extreme value distribution, including generalized linear modelling of each parameter. This function has the same structure as the gev.fit from ismev. Additionally it allows any parameter to be kept fixed and to not be estimated.

Usage

gevd.fit(
  xdat,
  ydat = NULL,
  mul = NULL,
  sigl = NULL,
  shl = NULL,
  mulink = identity,
  siglink = identity,
  shlink = identity,
  muinit = NULL,
  siginit = NULL,
  shinit = NULL,
  show = TRUE,
  method = "Nelder-Mead",
  optimPars = NULL,
  maxit = 10000,
  fixedPars = list(mu = NULL, sig = NULL, sh = NULL),
  ...
)

Arguments

xdat	A numeric vector of data to be fitted
ydat	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 xdat
mul	Numeric vectors of integers, giving the columns of ydat that contain covariates for generalized linear modelling of the location parameter (or NULL (the default) if the corresponding parameter is stationary)
sigl	As mul for the scale parameter
shl	As mul for the shape parameter
mulink	the link function for the location parameter - default to identity
siglink	the link function for the scale parameter - default to identity
shlink	the link function for the shape parameter - default to identity
muinit	initial values for the location parameter
siginit	initial values for the scale parameter
shinit	initial values for the shape parameter
show	Logical; if TRUE (the default), print details of the fit.
method	The optimization method (see optim for details).
optimPars	A string with other parameters to pass into optim. For example, depending on method, one could have "lower = 10, upper = 20"
maxit	The maximum number of iterations
fixedPars	a named list to fix any of the distribution parameter to a given value. When the named parameter is set to NULL its value is estimated.
...	Other control parameters for the optimization. These are passed to components of the control argument of optim.

Details

The form of the GEV used is that of Coles (2001) Eq (3.2) - so it is not the same as the one used in dgev. Specifically, positive values of the shape parameter imply a heavy tail, and negative values imply a bounded upper tail.

Value

An object of the gev.fit class as for objects obtained using ismev::gev.fit, so that ismev functions for gev.fit work on these objects when no parameter is kept fixed (i.e. fixedPars is a list of NULL)

References

Hosking, J.R.M. and Wallis, J.R., 2005. Regional frequency analysis: an approach based on L-moments. Cambridge university press.

Coles, S., 2001. An introduction to statistical modeling of extreme values. London: Springer.

See Also

dgev

Examples

set.seed(12)
x <- runif(500)
y <- rgev(500,loc = 40+4*x,scale = 6,sh = 0.2)
fit1 <- gevd.fit(y, show=FALSE)
fit1
## now add a regression model for the location
fit2 <- gevd.fit(y, ydat = cbind(x), mul=1, show=FALSE)
fit2
## now a fit with a fixed shape parameter (notice the sign)
fitf <- gevd.fit(y, show=FALSE, fixedPars = list(sh = -0.2))
fitf ## only two parameters are estimated 

ilapros/ilaprosUtils documentation built on April 6, 2023, 4:44 a.m.