VGAM (version 0.7-9)

Maxwell: The Maxwell Distribution

Description

Density, and distribution function 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, red 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="red")
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)
pmaxwell(Q, a) - probs    # Should be all zero