VGAM (version 1.1-8)

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)

Value

drayleigh gives the density,

prayleigh gives the distribution function,

qrayleigh gives the quantile function, and

rrayleigh generates random deviates.

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.

Author

T. W. Yee and Kai Huang

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.

See Also

rayleigh, maxwell.

Examples

if (FALSE)  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; red = 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 = 2, lty = 3, type = "h")
lines(x, prayleigh(x, scale = Scale), col = "red")