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.

### See Also

`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

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