The 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)
qrayleigh(p, scale = 1)
rrayleigh(n, scale = 1)

Arguments

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.

Value

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

Note

The Rayleigh distribution is related to the Maxwell distribution.

Author(s)

T. W. Yee

References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

See Also

rayleigh, maxwell.

Examples

## 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") 
## End(Not run)