forder {evd}

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 jth largest (default) or smallest of mlen, according to the value of largest.

largest

Logical; if TRUE (default) use the jth largest order statistic, otherwise use the jth 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.

See Also

anova.evd, fextreme, optim

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)