evd: forder – R documentation

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forder

Maximum-likelihood Fitting of Order Statistics

Description

Maximum-likelihood fitting for the distribution of a selected order statistic of a given number of independent variables from a specified distribution.

Usage

forder(x, start, densfun, distnfun, ..., distn, mlen = 1, j = 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 and functions are formed upon the addition of the prefixes `d` and `p` respectively.
`mlen`	The number of independent variables.
`j`	The order statistic, taken as the `j`th largest (default) or smallest of `mlen`, according to the value of `largest`.
`largest`	Logical; if `TRUE` (default) use the `j`th largest order statistic, otherwise use the `j`th smallest.
`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"). This class is defined in fextreme.

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.

Examples

uvd <- rorder(100, qnorm, mean = 0.56, mlen = 365, j = 2)
forder(uvd, list(mean = 0, sd = 1), distn = "norm", mlen = 365, j = 2)
forder(uvd, list(rate = 1), distn = "exp", mlen = 365, j = 2,
  method = "Brent", lower=0.01, upper=10)
forder(uvd, list(scale = 1), shape = 1, distn = "gamma", mlen = 365, j = 2,
  method = "Brent", lower=0.01, upper=10)
forder(uvd, list(shape = 1, scale = 1), distn = "gamma", mlen = 365, j = 2)

evd

Functions for Extreme Value Distributions

v2.3-3

GPL-3

Authors

Alec Stephenson. Function fbvpot by Chris Ferro.

Initial release

2018-04-25