VGAM (version 0.7-9)

Kumar: The Kumaraswamy Distribution

Description

Density, distribution function, quantile function and random generation for the Kumaraswamy distribution.

Usage

dkumar(x, shape1, shape2, log=FALSE)
pkumar(q, shape1, shape2)
qkumar(p, shape1, shape2)
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.

Value

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

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

shape1 = 2; shape2 = 2; nn = 201; # shape1 = shape2 = 0.5;
x = seq(0.0 , 1.00, len=nn)
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, red is cumulative distribution function",
     sub="Purple lines are the 10,20,...,90 percentiles")
lines(x, pkumar(x, shape1, shape2), col="red")
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