Gumbel {DescTools} 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(z) = \exp\left\{-\exp\left[-\left(\frac{z-a}{b}\right) \right]\right\}

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.

### Author(s)

Alec Stephenson <alec_stephenson@hotmail.com>

rFrechet, rGenExtrVal, rRevWeibull

### 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 DescTools version 0.99.54 Index]