gumbel {evd} R Documentation

## The Gumbel Distribution

### Description

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

### Usage

```dgumbel(x, loc=0, scale=1, log = FALSE)
pgumbel(q, loc=0, scale=1, lower.tail = TRUE)
qgumbel(p, loc=0, scale=1, lower.tail = TRUE)
rgumbel(n, loc=0, scale=1)
```

### Arguments

 `x, q` Vector of quantiles. `p` Vector of probabilities. `n` Number of observations. `loc, scale` Location and scale parameters (can be given as vectors). `log` Logical; if `TRUE`, the log density is returned. `lower.tail` Logical; if `TRUE` (default), probabilities are P[X <= x], otherwise, P[X > x]

### Details

The Gumbel distribution function with parameters `loc` = a and `scale` = b is

G(x) = exp{-exp[-(z-a)/b]}

for all real z, where b > 0.

### Value

`dgumbel` gives the density function, `pgumbel` gives the distribution function, `qgumbel` gives the quantile function, and `rgumbel` generates random deviates.

### Interesting Fact

Gumbel is the name of my teddy bear. And a famous statistician.

`rfrechet`, `rgev`, `rrweibull`

### Examples

```dgumbel(-1:2, -1, 0.5)
pgumbel(-1:2, -1, 0.5)
qgumbel(seq(0.9, 0.6, -0.1), 2, 0.5)
rgumbel(6, -1, 0.5)
p <- (1:9)/10
pgumbel(qgumbel(p, -1, 2), -1, 2)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
```

[Package evd version 2.2-4 Index]