gumbelIIUC: The Gumbel-II Distribution

Description Usage Arguments Details Value Author(s) See Also Examples

Description

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

Usage

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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

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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", las = 1,
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple 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 = "purple", lty = 3, type = "h")
pgumbelII(Q, shape = Shape, Scale) - probs # Should be all zero
abline(h = probs, col = "purple", lty = 3) 
## End(Not run)

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.