# maxwellUC: The Maxwell Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```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.

`maxwell`, `Rayleigh`, `rayleigh`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```## 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) ```