VGAM (version 0.8-3)

Maxwell: The Maxwell Distribution

Description

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

Usage

dmaxwell(x, a, log = FALSE)
pmaxwell(q, a)
qmaxwell(p, a)
rmaxwell(n, a)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. A single positive integer.

a

the parameter.

log

Logical. If log = TRUE then the logarithm of the density is returned.

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 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

a <- 3; x <- seq(-0.5, 3, len = 100)
plot(x, dmaxwell(x, a = a), type = "l", col = "blue", las = 1, ylab = "",
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles")
abline(h = 0, col = "blue", lty = 2)
lines(x, pmaxwell(x, a = a), type = "l", col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qmaxwell(probs, a = a)
lines(Q, dmaxwell(Q, a), col = "purple", lty = 3, type = "h")
lines(Q, pmaxwell(Q, a), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pmaxwell(Q, a) - probs))  # Should be zero