evd (version 1.2-3)

gumbel: The Gumbel Distribution

Description

Density, 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, 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 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