Maxwell {VGAM}

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",
     main = "Blue is density, orange is CDF", ylab = "", las = 1,
     sub = "Purple lines are the 10,20,...,90 percentiles")
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)