VGAM (version 1.1-1)

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.

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
# }