evd (version 1.2-3)

forder: Maximum-likelihood Fitting of Order Statistics

Description

Maximum-likelihood fitting for the distribution of a given order statistic of a sample from any specified distribution function.

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 parameters to be optimized with initial values.

densfun, distnfun

Density and distribution function of the specified distribution.

...

Additional parameters, either for the specified distribution or for optim. If parameters of the distribution are included they will be held fixed. If parameters of the distribution are not included either here or as a named compon

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 re

mlen

The size of the random sample.

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).

Value

• Returns an object of class "evd".

  The generic accessor functions fitted (or fitted.values), std.errors and deviance extract various features of the returned object. The function anova compares nested models. An object of class "evd" is a list containing at least 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.
• model
  A character string describing the fitted model.

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.

Although j can be any integer in $[1,\code{mlen}]$ it is preferable, for computational reasons, to specify j in the interval $[1,\code{ceiling}(\code{mlen}/2)]$, which can always be achieved using the argument largest.

See Also

anova.evd, fext, optim

Examples

uvdata <- rorder(100, qnorm, mean = 0.56, mlen = 365, j = 2)
forder(uvdata, list(mean = 0, sd = 1), distn = "norm", mlen = 365, j = 2)
forder(uvdata, list(rate = 1), distn = "exp", mlen = 365, j = 2)
forder(uvdata, list(scale = 1), shape = 1, distn = "gamma", mlen = 365,
j = 2)
forder(uvdata, list(shape = 1, scale = 1), distn = "gamma", mlen = 365,
j = 2)