Rayleigh distribution
Density, distribution function, quantile function and random generation for the Rayleigh distribution.
drayleigh(x, sigma = 1, log = FALSE) prayleigh(q, sigma = 1, lower.tail = TRUE, log.p = FALSE) qrayleigh(p, sigma = 1, lower.tail = TRUE, log.p = FALSE) rrayleigh(n, sigma = 1)
x, q |
vector of quantiles. |
sigma |
positive valued parameter. |
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) = x/σ^2 * exp(-(x^2 / 2*σ^2))
Cumulative distribution function
F(x) = 1 - exp(-x^2 / 2*σ^2)
Quantile function
F^-1(p) = sqrt(-2*σ^2 * log(1-p))
Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC.
Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.
x <- rrayleigh(1e5, 13) hist(x, 100, freq = FALSE) curve(drayleigh(x, 13), 0, 60, col = "red", add = TRUE) hist(prayleigh(x, 13)) plot(ecdf(x)) curve(prayleigh(x, 13), 0, 60, col = "red", lwd = 2, add = TRUE)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.