maxwell {VGAM}R Documentation

Maxwell Distribution Family Function

Description

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

Usage

maxwell(link = "loge")

Arguments

link Parameter link function applied to the parameter a. See Links for more choices. A log link is the default because the parameter is positive.

Details

The Maxwell distribution, which is used in the area of thermodynamics, has a probability density function that can be written

f(y) = 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).

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, rrvglm and vgam.

Note

A related distribution is the Rayleigh distribution.

Author(s)

T. W. Yee

References

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

See Also

Maxwell, rayleigh.

Examples

y = rmaxwell(n <- 1000, a=exp(2))
fit = vglm(y ~ 1, maxwell, trace=TRUE, crit="c")
coef(fit, matrix=TRUE)
Coef(fit)

[Package VGAM version 0.7-1 Index]