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