# Rayleigh: Rayleigh distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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

 ```1 2 3 4 5 6``` ```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.