Rayleigh Distribution

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.

References

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

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 \(b\).

Note

The Rayleigh distribution is related to the Maxwell distribution.

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")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'y' in selecting a method for function 'plot': object 'Scale' not found
abline(h = 0, col = "blue", lty = 2)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
qq <- qrayleigh(seq(0.1, 0.9, by = 0.1), scale = Scale)
#> Error: object 'Scale' not found
lines(qq, drayleigh(qq, scale = Scale), col = 2, lty = 3, type = "h")
#> Error: object 'qq' not found
lines(x, prayleigh(x, scale = Scale), col = "red")  # \dontrun{}
#> Error: object 'Scale' not found