fextreme: Maximum-likelihood Fitting of Maxima and Minima

In evd: Functions for Extreme Value Distributions

Maximum-likelihood Fitting of Maxima and Minima

Description

Maximum-likelihood fitting for the distribution of the maximum/minimum of a given number of independent variables from a specified distribution.

Usage

fextreme(x, start, densfun, distnfun, ..., distn, mlen = 1, largest =
    TRUE, std.err = TRUE, corr = FALSE, method = "Nelder-Mead")

Arguments

x	A numeric vector.
start	A named list giving the initial values for the parameters over which the likelihood is to be maximized.
densfun, distnfun	Density and distribution function of the specified distribution.
...	Additional parameters, either for the specified distribution or for the optimization function optim. If parameters of the distribution are included they will be held fixed at the values given (see Examples). If parameters of the distribution are not included either here or as a named component in start they will be held fixed at the default values specified in the corresponding density and distribution functions (assuming they exist; an error will be generated otherwise).
distn	A character string, optionally specified as an alternative to densfun and distnfun such that the density and distribution functions are formed upon the addition of the prefixes d and p respectively.
mlen	The number of independent variables.
largest	Logical; if TRUE (default) use maxima, otherwise minima.
std.err	Logical; if TRUE (the default), the standard errors are returned.
corr	Logical; if TRUE, the correlation matrix is returned.
method	The optimization method (see optim for details).

Details

Maximization of the log-likelihood is performed. The estimated standard errors are taken from the observed information, calculated by a numerical approximation.

If the density and distribution functions are user defined, the order of the arguments must mimic those in R base (i.e. data first, parameters second). Density functions must have log arguments.

Value

Returns an object of class c("extreme","evd").

The generic accessor functions fitted (or fitted.values), std.errors, deviance, logLik and AIC extract various features of the returned object. The function anova compares nested models.

An object of class c("extreme","evd") is a list containing at most the following components

estimate	A vector containing the maximum likelihood estimates.
std.err	A vector containing the standard errors.
deviance	The deviance at the maximum likelihood estimates.
corr	The correlation matrix.
var.cov	The variance covariance matrix.
convergence, counts, message	Components taken from the list returned by optim.
call	The call of the current function.
data	The data passed to the argument x.
n	The length of x.

See Also

anova.evd, forder, optim

Examples

uvdata <- rextreme(100, qnorm, mean = 0.56, mlen = 365)
fextreme(uvdata, list(mean = 0, sd = 1), distn = "norm", mlen = 365)
fextreme(uvdata, list(rate = 1), distn = "exp", mlen = 365, 
  method = "Brent", lower=0.01, upper=10)
fextreme(uvdata, list(scale = 1), shape = 1, distn = "gamma", mlen = 365,
  method = "Brent", lower=0.01, upper=10)
fextreme(uvdata, list(shape = 1, scale = 1), distn = "gamma", mlen = 365)

evd documentation built on Sept. 21, 2024, 9:06 a.m.