# extreme: Distributions of Maxima and Minima In evd: Functions for Extreme Value Distributions

## Description

Density function, distribution function, quantile function and random generation for the maximum/minimum of a given number of independent variables from a specified distribution.

## Usage

 ```1 2 3 4 5 6 7``` ```dextreme(x, densfun, distnfun, ..., distn, mlen = 1, largest = TRUE, log = FALSE) pextreme(q, distnfun, ..., distn, mlen = 1, largest = TRUE, lower.tail = TRUE) qextreme(p, quantfun, ..., distn, mlen = 1, largest = TRUE, lower.tail = TRUE) rextreme(n, quantfun, ..., distn, mlen = 1, largest = TRUE) ```

## Arguments

 `x, q` Vector of quantiles. `p` Vector of probabilities. `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 given 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. `largest` Logical; if `TRUE` (default) use maxima, otherwise minima. `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

`dextreme` gives the density function, `pextreme` gives the distribution function and `qextreme` gives the quantile function of the maximum/minimum of `mlen` independent variables from a specified distibution. `rextreme` generates random deviates.

`rgev`, `rorder`
 ```1 2 3 4 5 6 7 8 9``` ```dextreme(2:4, dnorm, pnorm, mean = 0.5, sd = 1.2, mlen = 5) dextreme(2:4, distn = "norm", mean = 0.5, sd = 1.2, mlen = 5) dextreme(2:4, distn = "exp", mlen = 2, largest = FALSE) pextreme(2:4, distn = "exp", rate = 1.2, mlen = 2) qextreme(seq(0.9, 0.6, -0.1), distn = "exp", rate = 1.2, mlen = 2) rextreme(5, qgamma, shape = 1, mlen = 10) p <- (1:9)/10 pexp(qextreme(p, distn = "exp", rate = 1.2, mlen = 1), rate = 1.2) ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ```