VGAM (version 1.0-2)

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, lower.tail = TRUE, log.p = FALSE)
qkumar(p, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
rkumar(n, shape1, shape2)

Arguments

lshape1, lshape2

Link function for the two positive shape parameters, respectively, called $a$ and $b$ below. See Links for more choices.

ishape1, ishape2

Numeric. Optional initial values for the two positive shape parameters.

tol12

Numeric and positive. Tolerance for testing whether the second shape parameter is either 1 or 2. If so then the working weights need to handle these singularities.

grid.shape1

Lower and upper limits for a grid search for the first shape parameter.

zero

See CommonVGAMffArguments.

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.

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

## 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)