VGAM (version 1.1-14)

maxwell: Maxwell Regression Family Function

Description

Estimating the parameter of the Maxwell distribution by maximum likelihood estimation.

Usage

maxwell(link = "loglink", zero = NULL, parallel = FALSE,
        type.fitted = c("mean", "percentiles", "Qlink"),
        percentiles = 50)

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm,

rrvglm

and vgam.

Details

The Maxwell distribution, which is used in the area of thermodynamics, has a probability density function that can be written $$f(y;a) = \sqrt{2/\pi} a^{3/2} y^2 \exp(-0.5 a y^2)$$ for \(y>0\) and \(a>0\). The mean of \(Y\) is \(\sqrt{8 / (a \pi)}\) (returned as the fitted values), and its variance is \((3\pi - 8)/(\pi a)\).

References

von Seggern, D. H. (1993). CRC Standard Curves and Surfaces, Boca Raton, FL, USA: CRC Press.

See Also

Maxwell, rayleigh, poisson.points.

Examples

mdata <- data.frame(y = rmaxwell(1000, rate = exp(2)))
fit <- vglm(y ~ 1, maxwell, mdata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit)