VGAM (version 1.1-6)

# Rayleigh: Rayleigh Distribution

## Description

Density, distribution function, quantile function and random generation for the Rayleigh distribution with parameter `a`.

## Usage

```drayleigh(x, scale = 1, log = FALSE)
prayleigh(q, scale = 1, lower.tail = TRUE, log.p = FALSE)
qrayleigh(p, scale = 1, lower.tail = TRUE, log.p = FALSE)
rrayleigh(n, scale = 1)```

## Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Fed into `runif`.

scale

the scale parameter \(b\).

log

Logical. If `log = TRUE` then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in `pnorm` or `qnorm`.

## Value

`drayleigh` gives the density, `prayleigh` gives the distribution function, `qrayleigh` gives the quantile function, and `rrayleigh` generates random deviates.

## Details

See `rayleigh`, the VGAM family function for estimating the scale parameter \(b\) by maximum likelihood estimation, for the formula of the probability density function and range restrictions on the parameter \(b\).

## References

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

`rayleigh`, `maxwell`.

## Examples

Run this code
``````# NOT RUN {
Scale <- 2; x <- seq(-1, 8, by = 0.1)
plot(x, drayleigh(x, scale = Scale), type = "l", ylim = c(0,1),
las = 1, ylab = "",
main = "Rayleigh density divided into 10 equal areas; orange = cdf")
abline(h = 0, col = "blue", lty = 2)
qq <- qrayleigh(seq(0.1, 0.9, by = 0.1), scale = Scale)
lines(qq, drayleigh(qq, scale = Scale), col = "purple", lty = 3, type = "h")
lines(x, prayleigh(x, scale = Scale), col = "orange")
# }
``````

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