Rayleigh {VGAM} | R Documentation

## The Rayleigh Distribution

### Description

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

### Usage

    drayleigh(x, a, log=FALSE)
    prayleigh(q, a)
    qrayleigh(p, a)
    rrayleigh(n, a)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Must be a positive integer of length 1.
`a` | the parameter a.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### Details

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

### 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:
    a = 2
    x = seq(-1, 8, by=0.1)
    plot(x, drayleigh(x, a=a), 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),a=a)
    lines(qq, drayleigh(qq, a=a), col="purple", lty=3, type="h")
    lines(x, prayleigh(x, a=a), col="red")
    ## End(Not run)

[Package VGAM version 0.7-9 Index]