fextreme {evd} | R Documentation

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

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