Kumaraswamy: Kumaraswamy distribution

In extraDistr: Additional Univariate and Multivariate Distributions

Kumaraswamy distribution

Description

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

Usage

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 \le 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) = abx^{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

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 May 29, 2024, 9:31 a.m.