An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
Details
The 3-parameter Dagum distribution is the 4-parameter
generalized beta II distribution with shape parameter $q=1$.
It is known under various other names, such as the Burr III, inverse Burr,
beta-K, and 3-parameter kappa distribution.
It can be considered a generalized log-logistic distribution.
Some distributions which are special cases of the 3-parameter Dagum
are the inverse Lomax ($a=1$), Fisk ($p=1$),
and the inverse paralogistic ($a=p$).
More details can be found in Kleiber and Kotz (2003).
The Dagum distribution has a cumulative distribution function
$$F(y) = [1 + (y/b)^{-a}]^{-p}$$
which leads to a probability density function
$$f(y) = ap y^{ap-1} / [b^{ap} {1 + (y/b)^a}^{p+1}]$$
for $a > 0$, $b > 0$, $p > 0$, $y > 0$.
Here, $b$ is the scale parameter scale,
and the others are shape parameters.
The mean is
$$E(Y) = b \, \Gamma(p + 1/a) \, \Gamma(1 - 1/a) / \Gamma(p)$$
provided $-ap < 1 < a$.
References
Kleiber, C. and Kotz, S. (2003)
Statistical Size Distributions in Economics and
Actuarial Sciences,
Hoboken, NJ: Wiley-Interscience.