Power distribution
Density, distribution function, quantile function and random generation for the power distribution.
dpower(x, alpha, beta, log = FALSE) ppower(q, alpha, beta, lower.tail = TRUE, log.p = FALSE) qpower(p, alpha, beta, lower.tail = TRUE, log.p = FALSE) rpower(n, alpha, beta)
x, q |
vector of quantiles. |
alpha, beta |
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) = (β*x^(β-1)) / (α^β)
Cumulative distribution function
F(x) = x^β / α^β
Quantile function
F^-1(p) = α * p^(1/β)
x <- rpower(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dpower(x, 5, 16), 2, 6, col = "red", add = TRUE, n = 5000) hist(ppower(x, 5, 16)) plot(ecdf(x)) curve(ppower(x, 5, 16), 2, 6, col = "red", lwd = 2, add = TRUE)
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