evd: fextreme – R documentation

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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 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`.

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

Functions for Extreme Value Distributions

v2.3-3

GPL-3

Authors

Alec Stephenson. Function fbvpot by Chris Ferro.

Initial release

2018-04-25