An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
Arguments
lscale, lshape3.q
Parameter link function applied to the
(positive) parameters scale and q.
See Links for more choices.
iscale, ishape3.q, imethod
See CommonVGAMffArguments for information.
For imethod = 2 a good initial value for
iscale is needed to obtain a good estimate for
the other parameter.
gscale, gshape3.q, zero, probs.y
See
CommonVGAMffArguments.
Author
T. W. Yee
Details
The 2-parameter Lomax distribution is the 4-parameter
generalized beta II distribution with shape parameters \(a=p=1\).
It is probably more widely known as the Pareto (II) distribution.
It is also the 3-parameter Singh-Maddala distribution
with shape parameter \(a=1\), as well as the
beta distribution of the second kind with \(p=1\).
More details can be found in Kleiber and Kotz (2003).
The Lomax distribution has density
$$f(y) = q / [b \{1 + y/b\}^{1+q}]$$
for \(b > 0\), \(q > 0\), \(y \geq 0\).
Here, \(b\) is the scale parameter scale,
and q is a shape parameter.
The cumulative distribution function is
$$F(y) = 1 - [1 + (y/b)]^{-q}.$$
The mean is
$$E(Y) = b/(q-1)$$
provided \(q > 1\); these are returned as the fitted values.
This family function handles multiple responses.
References
Kleiber, C. and Kotz, S. (2003).
Statistical Size Distributions in Economics and
Actuarial Sciences,
Hoboken, NJ, USA: Wiley-Interscience.