# Kumaraswamy: Kumaraswamy distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```dkumar(x, a = 1, b = 1, log = FALSE) pkumar(q, a = 1, b = 1, lower.tail = TRUE, log.p = FALSE) qkumar(p, a = 1, b = 1, lower.tail = TRUE, log.p = FALSE) rkumar(n, a = 1, b = 1) ```

## Arguments

 `x, q` vector of quantiles. `a, b` positive valued parameters. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]. `p` vector of probabilities. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required.

## Details

Probability density function

f(x) = a*b*x^(a-1)*(1-x^a)^(b-1)

Cumulative distribution function

F(x) = 1-(1-x^a)^b

Quantile function

F^-1(p) = 1-(1-p^(1/b))^(1/a)

## References

Jones, M. C. (2009). Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6, 70-81.

Cordeiro, G.M. and de Castro, M. (2009). A new family of generalized distributions. Journal of Statistical Computation & Simulation, 1-17.

## Examples

 ```1 2 3 4 5 6``` ```x <- rkumar(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dkumar(x, 5, 16), 0, 1, col = "red", add = TRUE) hist(pkumar(x, 5, 16)) plot(ecdf(x)) curve(pkumar(x, 5, 16), 0, 1, col = "red", lwd = 2, add = TRUE) ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.