Gumbel-II {VGAM} | R Documentation |
Density, cumulative distribution function, quantile function and random generation for the Gumbel-II distribution.
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)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Same as in |
log |
Logical.
If |
lower.tail, log.p |
|
shape, scale |
positive shape and scale parameters. |
See gumbelII
for details.
dgumbelII
gives the density,
pgumbelII
gives the cumulative distribution function,
qgumbelII
gives the quantile function, and
rgumbelII
generates random deviates.
T. W. Yee and Kai Huang
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)