evd (version 1.2-3)

order: Distributions of Order Statistics

Description

Density, distribution function and random generation for a selected order statistic of a sample of independent variables from a specified distribution.

Usage

dorder(x, densfun, distnfun, ..., distn, mlen = 1, j = 1,
      largest = TRUE, log = FALSE)
porder(q, distnfun, ..., distn, mlen = 1, j = 1, largest = TRUE,
      lower.tail = TRUE)  
rorder(n, quantfun, ..., distn, mlen = 1, j = 1, largest = TRUE)

Arguments

x, q

Vector of quantiles.

n

Number of observations.

densfun, distnfun, quantfun

Density, distribution and quantile function of the distribution.

...

Parameters of the distribution.

distn

A character string, optionally specified as an alternative to densfun, distnfun and quantfun such that the density, distribution and quantile functions are formed upon the addition of the prefixes d

mlen

The size of the sample from which the order statistic is taken.

j

The order statistic, taken as the jth largest (default) or smallest of mlen, according to the value of largest.

log

Logical; if TRUE, the log density is returned.

largest

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

lower.tail

Logical; if TRUE (default) probabilities are P[X <= x],="" otherwise="" p[x=""> x].

Value

• dorder gives the density, porder gives the distribution function and qorder gives the quantile function of a selected order statistic from a sample of size mlen, from a specified distibution. rorder generates random deviates.

Details

The density function must have a log argument (a simple wrapper can always be constructed to achieve this). If any parameter arguments are missing the default values (where they exist) in the density, distribution and quantile functions are used. 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

rext, rgev

Examples

dorder(2:4, dnorm, pnorm, mean = 0.5, sd = 1.2, mlen = 5, j = 2)
dorder(2:4, distn = "norm", mean = 0.5, sd = 1.2, mlen = 5, j = 2)
dorder(2:4, distn = "exp", mlen = 2, j = 2)
porder(2:4, distn = "exp", rate = 1.2, mlen = 2, j = 2)
rorder(5, qgamma, shape = 1, mlen = 10, j = 2)