"Reverse" Gumbel Distribution Functions

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

dRevGumbel (x, location = 0, scale = 1)
pRevGumbel (q, location = 0, scale = 1)
qRevGumbel (p, location = 0, scale = 1)
rRevGumbel (n, location = 0, scale = 1)

qRevGumbelExp(p)

Arguments

x, q

numeric vector of abscissa (or quantile) values at which to evaluate the density or distribution function.

p

numeric vector of probabilities at which to evaluate the quantile function.

location

location of the distribution

scale

scale (\(> 0\)) of the distribution.

n

number of random variates, i.e., length of resulting vector of rRevGumbel(..).

Value

a numeric vector, of the same length as x, q, or p for the first three functions, and of length n for rRevGumbel().

Author

Werner Stahel; partly inspired by package VGAM. Martin Maechler for numeric cosmetic.

See also

the Weibull distribution functions in R's stats package.

Examples

curve(pRevGumbel(x, scale= 1/2), -3,2, n=1001, col=1, lwd=2,
      main = "RevGumbel(x, scale = 1/2)")
abline(h=0:1, v = 0, lty=3, col = "gray30")
curve(dRevGumbel(x, scale= 1/2),       n=1001, add=TRUE,
      col = (col.d <- adjustcolor(2, 0.5)), lwd=3)
legend("left", c("cdf","pdf"), col=c("black", col.d), lwd=2:3, bty="n")


med <- qRevGumbel(0.5, scale=1/2)
cat("The median is:",  format(med),"\n")
#> The median is: -0.1832565