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

Usage

maxwell(link = "loge", zero = NULL)

Arguments

link, zero

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.

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.: CRC Press.