# gumbel: The Gumbel Distribution In RcmdrMisc: R Commander Miscellaneous Functions

## Description

Density, distribution function, quantile function and random generation for the Gumbel distribution with specified `location` and `scale` parameters.

## Usage

 ```1 2 3 4``` ```dgumbel(x, location = 0, scale = 1) pgumbel(q, location=0, scale=1, lower.tail=TRUE) qgumbel(p, location=0, scale=1, lower.tail=TRUE) rgumbel(n, location=0, scale=1) ```

## Arguments

 `x, q` vector of quantiles (values of the variable). `p` vector of probabilities. `n` number of observations. If `length(n)` > 1, the length is taken to be the number required. `location` location parameter (default `0`); potentially a vector. `scale` scale parameter (default `1`); potentially a vector. `lower.tail` logical; if `TRUE` (the default) probabilities and quantiles correspond to P(X ≤ x), if `FALSE` to P(X > x).

## Author(s)

John Fox jfox@mcmaster.ca

## References

See https://en.wikipedia.org/wiki/Gumbel_distribution for details of the Gumbel distribution.

## Examples

 ```1 2 3 4 5 6 7 8``` ```x <- 100 + 5*c(-Inf, -1, 0, 1, 2, 3, Inf, NA) dgumbel(x, 100, 5) pgumbel(x, 100, 5) p <- c(0, .25, .5, .75, 1, NA) qgumbel(p, 100, 5) summary(rgumbel(1e5, 100, 5)) ```

### Example output

```Loading required package: car