fextreme: 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")

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.

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.

Examples

Run this code

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)

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