evd (version 2.1-0)

gumbel: 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]

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.

Details

The Gumbel distribution function with parameters $\code{loc} = a$ and $\code{scale} = b$ is $$G(z) = \exp\left{-\exp\left[-\left(\frac{z-a}{b}\right) \right]\right}$$ for all real $z$, where $b > 0$.

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