R: The Maxwell Distribution

Maxwell {VGAM} | R Documentation

## The Maxwell Distribution

### Description

Density, distribution function, quantile function and random generation for the Maxwell distribution.

### Usage

    dmaxwell(x, rate, log = FALSE)
    pmaxwell(q, rate, lower.tail = TRUE, log.p = FALSE)
    qmaxwell(p, rate, lower.tail = TRUE, log.p = FALSE)
    rmaxwell(n, rate)

### Arguments

`x, q, p, n` | Same as `Uniform`.
`rate` | the (rate) parameter.
`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 `maxwell`, the VGAM family function for estimating the (rate) parameter a by maximum likelihood estimation, for the formula of the probability density function.

### Value

`dmaxwell` gives the density, `pmaxwell` gives the distribution function, `qmaxwell` gives the quantile function, and `rmaxwell` generates random deviates.

### Note

The Maxwell distribution is related to the Rayleigh distribution.

### Author(s)

T. W. Yee and Kai Huang

### References

Balakrishnan, N. and Nevzorov, V. B. (2003). A Primer on Statistical Distributions. Hoboken, New Jersey: Wiley.

### See Also

`maxwell`, `Rayleigh`, `rayleigh`.

### Examples

    ## Not run:  rate <- 3; x <- seq(-0.5, 3, length = 100)
    plot(x, dmaxwell(x, rate = rate), type = "l", col = "blue", las = 1,
         main = "Blue is density, orange is cumulative distribution function",
         sub = "Purple lines are the 10,20,...,90 percentiles", ylab = "")
    abline(h = 0, col = "blue", lty = 2)
    lines(x, pmaxwell(x, rate = rate), type = "l", col = "orange")
    probs <- seq(0.1, 0.9, by = 0.1)
    Q <- qmaxwell(probs, rate = rate)
    lines(Q, dmaxwell(Q, rate), col = "purple", lty = 3, type = "h")
    lines(Q, pmaxwell(Q, rate), col = "purple", lty = 3, type = "h")
    abline(h = probs, col = "purple", lty = 3)
    max(abs(pmaxwell(Q, rate) - probs))  # Should be zero

    ## End(Not run)

[Package VGAM version 1.1-3 Index]