# Gumbel: The Gumbel Distribution In powdist: Power and Reversal Power Distributions

## Description

Density, distribution function, quantile function and random generation for the Gumbel distribution with parameters mu and sigma.

## Usage

 ```1 2 3 4 5 6 7``` ```dgumbel(x, mu = 0, sigma = 1, log = FALSE) pgumbel(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qgumbel(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rgumbel(n, mu = 0, sigma = 1) ```

## Arguments

 `x, q` vector of quantiles. `mu, sigma` location and scale parameters. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x ], otherwise, P[X > x]. `p` vector of probabilities. `n` number of observations.

## Details

The Gumbel distribution has density

f(x)=(1/σ)exp(-(x-μ)/σ-exp(-(x-μ)/σ)),

where -∞<μ<∞ is the location paramether and σ^2>0 is the scale parameter.

## Examples

 ```1 2 3 4``` ```dgumbel(1, 3, 4) pgumbel(1, 3, 4) qgumbel(0.2, 3, 4) rgumbel(5, 3, 4) ```

### Example output

``` 0.07926048
 0.1922956
 1.09646
  6.3854587  3.7480653 10.4243566  8.0340240  0.1384547
```

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