The Kumaraswamy Distribution
Density, distribution function, quantile function and random generation for the Kumaraswamy distribution.
dkumar(x, shape1, shape2, log = FALSE) pkumar(q, shape1, shape2, lower.tail = TRUE, log.p = FALSE) qkumar(p, shape1, shape2, lower.tail = TRUE, log.p = FALSE) rkumar(n, shape1, shape2)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
If |
shape1, shape2 |
positive shape parameters. |
log |
Logical.
If |
lower.tail, log.p |
See kumar, the VGAM family function
for estimating the parameters,
for the formula of the probability density function and other details.
dkumar gives the density,
pkumar gives the distribution function,
qkumar gives the quantile function, and
rkumar generates random deviates.
T. W. Yee and Kai Huang
## Not run:
shape1 <- 2; shape2 <- 2; nn <- 201; # shape1 <- shape2 <- 0.5;
x <- seq(-0.05, 1.05, len = nn)
plot(x, dkumar(x, shape1, shape2), type = "l", las = 1, ylim = c(0,1.5),
ylab = paste("fkumar(shape1 = ", shape1, ", shape2 = ", shape2, ")"),
col = "blue", cex.main = 0.8,
main = "Blue is density, orange is cumulative distribution function",
sub = "Purple lines are the 10,20,...,90 percentiles")
lines(x, pkumar(x, shape1, shape2), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qkumar(probs, shape1, shape2)
lines(Q, dkumar(Q, shape1, shape2), col = "purple", lty = 3, type = "h")
lines(Q, pkumar(Q, shape1, shape2), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pkumar(Q, shape1, shape2) - probs)) # Should be 0
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.