order {evd} | R Documentation

## Distributions of Order Statistics

### Description

Density function, distribution function and random generation for a selected order statistic of a given number 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 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 `densfun`, `distnfun` and `quantfun` 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 `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.
`log` | Logical; if `TRUE`, the log density is returned.
`lower.tail` | Logical; if `TRUE` (default) probabilities are P[X <= x], otherwise P[X > x].

### Value

`dorder` gives the density function, `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.

### See Also

`rextreme`, `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)

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