extreme {evd} | R Documentation

## Distributions of Maxima and Minima

### 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

    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.

### See Also

`rgev`, `rorder`

### Examples

    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)
    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

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