kappad.fit: Maximum Likelihood Fitting for the Kappa distribution
In ilapros/ilaprosUtils: A Miscellaneous Collection of Functions I Tend to Use

kappad.fit

R Documentation

Maximum Likelihood Fitting for the Kappa distribution

Description

Maximum-likelihood fitting for the Kappa distribution, including generalized linear modelling of each parameter. This function has the same structure as the gevd.fit and is inspired by ismev::gev.fit. The function allows any parameter to be kept fixed and to not be estimated.

Usage

kappad.fit(
  xdat,
  ydat = NULL,
  mul = NULL,
  sigl = NULL,
  shl = NULL,
  sh2l = NULL,
  mulink = identity,
  siglink = identity,
  shlink = identity,
  sh2link = identity,
  muinit = NULL,
  siginit = NULL,
  shinit = NULL,
  sh2init = NULL,
  show = TRUE,
  method = "Nelder-Mead",
  optimPars = NULL,
  maxit = 10000,
  fixedPars = list(mu = NULL, sig = NULL, sh = NULL, sh2 = 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
`sh2l`	As `mul` for the second 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
`sh2link`	the link function for the second 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
`sh2init`	initial values for the second 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 distribution is discussed in the Hosking and Wallis book and can be seen as a generelisation of several distributions used in extreme value modelling. Depending on the sh2 parameter value the Kappa distribution reduces to others commonly used distributions For example: when sh2 is equal to -1 the distribution reduces to a GLO, when sh2 is equal to 0 the distribution reduces to a GEV, when sh2 is equal to +1 the distribution reduces to a Generalised Pareto distribution (GPA).

Value

An object of the kappa.fit class - with values which mirror the ones of the gev.fit class in ismev

Examples

set.seed(12)
x <- runif(300)
y <- rkappa(300,loc = 40+4*x,scale = 6, sh = 0.2, sh2=-0.4)
fit1 <- kappad.fit(y, show=FALSE)
fit1
## now add a regression model for the location
fit2 <- kappad.fit(y, ydat = cbind(x), mul=1, show=FALSE)
fit2
## now a fit with a fixed shape parameter 
fitf <- kappad.fit(y, show=FALSE, fixedPars = list(sh = 0.2))
fitf ## only three parameters are estimated 
## could also fix the second shape parameter
#fitf2 <- kappad.fit(y, show=FALSE, fixedPars = list(sh2 = -0.4))
#fitf2 ## only three parameters are estimated

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