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
if (FALSE) 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)
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