maxwell {VGAM}R Documentation

Maxwell Distribution Family Function

Description

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

Usage

maxwell(link = "loge", earg = list())

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.

earg

List. Extra argument for the link. See earg in Links for general information.

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).

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. Fisher-scoring and Newton-Raphson are the same here.

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

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

[Package VGAM version 0.8-4 Index]