Maxwell {VGAM}R Documentation

The Maxwell Distribution

Description

Density, and distribution function for the Maxwell distribution.

Usage

dmaxwell(x, a)
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.

Details

See maxwell, the VGAM family function for estimating the 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

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: 
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
## End(Not run)

[Package VGAM version 0.7-7 Index]