Kumar {VGAM} | R Documentation

## 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.

### Details

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

### Value

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

### Author(s)

T. W. Yee

### See Also

`kumar`.

### Examples

    ## Not run:
    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
    ## End(Not run)

[Package VGAM version 0.7-9 Index]