
dgumbelII(x, shape, scale = 1, log = FALSE)
pgumbelII(q, shape, scale = 1)
qgumbelII(p, shape, scale = 1)
rgumbelII(n, shape, scale = 1)
log = TRUE
then the logarithm of the density is returned.dgumbelII
gives the density,
pgumbelII
gives the cumulative distribution function,
qgumbelII
gives the quantile function, and
rgumbelII
generates random deviates.gumbelII
for details.gumbelII
,
dgumbel
.probs <- seq(0.01, 0.99, by = 0.01)
Shape <- exp( 0.5); Scale <- exp(1);
max(abs(pgumbelII(qgumbelII(p = probs, Shape, Scale),
Shape, Scale) - probs)) # Should be 0
x <- seq(-0.1, 10, by = 0.01);
plot(x, dgumbelII(x, 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, Scale), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qgumbelII(probs, Shape, Scale)
lines(Q, dgumbelII(Q, Shape, Scale), col = "purple", lty = 3, type = "h")
pgumbelII(Q, Shape, Scale) - probs # Should be all zero
abline(h = probs, col = "purple", lty = 3)
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