VGAM (version 1.1-12)

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.

Arguments

link

Parameter link function applied to \(a\), which is called the parameter rate. See Links for more choices and information; a log link is the default because the parameter is positive. More information is at CommonVGAMffArguments.

zero, parallel

See CommonVGAMffArguments.

type.fitted, percentiles

See CommonVGAMffArguments for information. Using "Qlink" is for quantile-links in VGAMextra.

Author

T. W. Yee

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)