# order: Distributions of Order Statistics In evd: Functions for Extreme Value Distributions

## 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

 ```1 2 3 4 5``` ```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.

`rextreme`, `rgev`

## Examples

 ```1 2 3 4 5``` ```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) ```

### Example output

```[1] 0.2300687782 0.0133524232 0.0001663078
[1] 0.2300687782 0.0133524232 0.0001663078
[1] 0.0366312778 0.0049575044 0.0006709253
[1] 0.9917703 0.9992534 0.9999323
[1] 1.6998847 0.7715514 1.4049845 1.2972775 2.7045204
```

evd documentation built on May 1, 2019, 10:11 p.m.