# kumarUC: The Kumaraswamy Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```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`.

## 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 and Kai Huang

`kumar`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## 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) ```