evd (version 2.1-0)

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")

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 paramete

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 respec

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).

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.
• 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.

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.

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)
fextreme(uvdata, list(scale = 1), shape = 1, distn = "gamma", mlen = 365)
fextreme(uvdata, list(shape = 1, scale = 1), distn = "gamma", mlen = 365)