VGAM (version 1.1-6)

# Maxwell: 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`.

## Value

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

## 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.

## References

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

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

## Examples

Run this code
``````# 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
# }
``````

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