Gumbel-II {VGAM}

The Gumbel-II Distribution

Description

Density, cumulative distribution function, quantile function and random generation for the Gumbel-II distribution.

Usage

dgumbelII(x, scale = 1, shape, log = FALSE)
pgumbelII(q, scale = 1, shape, lower.tail = TRUE, log.p = FALSE)
qgumbelII(p, scale = 1, shape, lower.tail = TRUE, log.p = FALSE)
rgumbelII(n, scale = 1, shape)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Same as in runif.

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

shape, scale

positive shape and scale parameters.

Details

See gumbelII for details.

Value

dgumbelII gives the density, pgumbelII gives the cumulative distribution function, qgumbelII gives the quantile function, and rgumbelII generates random deviates.

Author(s)

T. W. Yee and Kai Huang

See Also

gumbelII, dgumbel.

Examples

probs <- seq(0.01, 0.99, by = 0.01)
Scale <- exp(1); Shape <- exp( 0.5);
max(abs(pgumbelII(qgumbelII(p = probs, shape = Shape, Scale),
                  shape = Shape, Scale) - probs))  # Should be 0

## Not run:  x <- seq(-0.1, 10, by = 0.01);
plot(x, dgumbelII(x, shape = Shape, Scale), type = "l", col = "blue",
     main = "Blue is density, orange is the CDF", las = 1,
     sub = "Red lines are the 10,20,...,90 percentiles",
     ylab = "", ylim = 0:1)
abline(h = 0, col = "blue", lty = 2)
lines(x, pgumbelII(x, shape = Shape, Scale), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qgumbelII(probs, shape = Shape, Scale)
lines(Q, dgumbelII(Q, Scale, Shape), col = "red", lty = 3, type = "h")
pgumbelII(Q, shape = Shape, Scale) - probs # Should be all zero
abline(h = probs, col = "red", lty = 3) 
## End(Not run)