Parameter link function applied to the
(positive) parameters scale and q.
See Links for more choices.
earg.scale, earg.q
List. Extra argument for each of the links.
See earg in Links for general information.
init.scale, init.q
Optional initial values for scale and q.
zero
An integer-valued vector specifying which
linear/additive predictors are modelled as intercepts only.
Here, the values must be from the set {1,2} which correspond to
scale, q, respectively.
Value
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
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 $b > 0$, $q > 0$, $y > 0$.
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 $q > 1$.
References
Kleiber, C. and Kotz, S. (2003)
Statistical Size Distributions in Economics and
Actuarial Sciences,
Hoboken, NJ: Wiley-Interscience.