Skip to contents

Distributions of Order Statistics

Source: R/dpqr-order.R
dpqr-order.Rd

Density, distribution, and random generation functions for a selected order statistic (the j-th largest or smallest value) from a sample of a given size drawn from any specified distribution, derived analytically using the beta distribution representation of order statistics.

Usage

dorder(x, dFun, pFun, ..., distn, mlen = 1, j = 1, largest = TRUE, log = FALSE)

porder(
  q,
  pFun,
  ...,
  distn,
  mlen = 1,
  j = 1,
  largest = TRUE,
  lower.tail = TRUE,
  log.p = FALSE
)

rorder(n, qFun, ..., distn, mlen = 1, j = 1, largest = TRUE)

Arguments

x, q

vector of quantiles.

dFun, pFun, qFun

density, distribution and quantile function of the specified distribution. The density function must have a log argument (a simple wrapper can always be constructed to achieve this).

...

parameters of the specified distribution.

distn

a character string, optionally specified as an alternative to dFun, pFun and qFun such that the density, distribution and quantile functions are formed upon the addition of the prefixes d, p and q 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.

log, log.p

logical; if TRUE, probabilities p are given as log(p) and the density is returned on the log scale.

lower.tail

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

n

number of observations.

Value

dorder() gives the density function and porder() gives the distribution function of a selected order statistic from a sample of size mlen, from a specified distribution. rorder() generates random deviates. There is no quantile function for order statistics (qorder() does not exist).

Note

Based on code by Alec Stephenson previously published in the evd package, adapted to conform to package standards.

See also

distributions-overview

Examples


dorder(2:4, dnorm, pnorm, mean = 0.5, sd = 1.2, mlen = 5, j = 2)
#> [1] 0.2300687782 0.0133524232 0.0001663078
dorder(2:4, distn = "norm", mean = 0.5, sd = 1.2, mlen = 5, j = 2)
#> [1] 0.2300687782 0.0133524232 0.0001663078
dorder(2:4, distn = "exp", mlen = 2, j = 2)
#> [1] 0.0366312778 0.0049575044 0.0006709253
porder(2:4, distn = "exp", rate = 1.2, mlen = 2, j = 2)
#> [1] 0.9917703 0.9992534 0.9999323
rorder(5, qgamma, shape = 1, mlen = 10, j = 2)
#> [1] 1.0699673 0.9894456 1.9396696 1.7528036 2.2440109