VGAM: rayleighUC – R documentation

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rayleighUC

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`.

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 and Kai Huang

References

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

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)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13