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)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1 then the length is taken to be the number required.

shape1, shape2

positive shape parameters.

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Value

dkumar gives the density, pkumar gives the distribution function, qkumar gives the quantile function, and rkumar generates random deviates.

Author

T. W. Yee and Kai Huang

Details

See kumar, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

See also

kumar.

Examples

if (FALSE) { # \dontrun{
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, 
     ylab = paste("dkumar(shape1 = ", shape1,
                  ", shape2 = ", shape2, ")"),
     col = "blue", cex.main = 0.8, ylim = c(0,1.5),
     main = "Blue is density, orange is the CDF",
     sub = "Red 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 = "red", lty = 3, type = "h")
lines(Q, pkumar(Q, shape1, shape2), col = "red", lty = 3, type = "h")
abline(h = probs, col = "red", lty = 3)
max(abs(pkumar(Q, shape1, shape2) - probs))  # Should be 0
} # }