(see vglmff-class).
The object is used by modelling functions
such as vglm,
and vgam.
Arguments
lshape, gshape
Details at CommonVGAMffArguments.
The CIA link is loglink,
for shape approaching unity.
zero, parallel
Details at CommonVGAMffArguments.
type.fitted, percentiles
See CommonVGAMffArguments for information.
Using "Qlink" is for quantile-links in VGAMextra.
Author
T. W. Yee
Details
The Topple distribution
has a probability density function that can be written
$$f(y;s) = 2 s (1 - y) [y (2-y)]^{s-1}$$
for \(0<y<1\) and shape parameter \(0<s<1\).
The mean of \(Y\) is
\(1 - 4^s [\Gamma(1+s)]^2 / \Gamma(2 + 2s)\)
(returned as the fitted values).
References
Topp, C. W. and F. C. Leone (1955).
A family of J-shaped frequency functions.
Journal of the American Statistical Association,
50, 209--219.