An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm
and vgam.
Warning
Numerically, this distribution can be difficult to fit because of a
log-likelihood having multiple maxima.
The user is therefore encouraged to try different starting values,
i.e., make use of imu and irho.
Details
The two-parameter cardioid distribution
has a density that can be written as
$$f(y;\mu,\rho) = \frac{1}{2\pi}
\left(1 + 2\, \rho \cos(y - \mu) \right)$$
where $0 < y < 2\pi$,
$0 < \mu < 2\pi$, and
$-0.5 < \rho < 0.5$ is the concentration parameter.
The default link functions enforce the range constraints
of the parameters.
For positive $\rho$ the distribution is unimodal and symmetric about
$\mu$.
The mean of $Y$ (which make up the fitted values) is
$\pi + (\rho/\pi) ((2 \pi-\mu) \sin(2 \pi-\mu) +
\cos(2 \pi-\mu) - \mu \sin(\mu) - \cos(\mu))$.
References
Jammalamadaka, S. R. and SenGupta, A. (2001)
Topics in Circular Statistics,
Singapore: World Scientific.