Rayleigh: Rayleigh distribution

In extraDistr: Additional Univariate and Multivariate Distributions

Description

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

Usage

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)

Arguments

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 length(n) > 1, the length is taken to be the number required.

Details

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))

References

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.

Examples

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) 

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