VGAM (version 1.1-9)

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)

Value

dmaxwell gives the density,

pmaxwell gives the distribution function,

qmaxwell gives the quantile function, and

rmaxwell generates random deviates.

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.

Author

T. W. Yee and Kai Huang

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

if (FALSE)  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