Recently, several models have been proposed in literature for analyzing
ranks assigned by people to some object. These models summarize the liking feeling
for this object, possibly also with respect to a set of explanatory variables. Some
recent works have suggested the use of the Shifted Binomial and of the Inverse Hypergeometric
distribution for modelling the approval rate, while mixture models
have been developed for taking into account the uncertainty of the ranking process.
We propose two new probabilistic models, based on the Discrete Beta and the
Shifted-Beta Binomial distributions, that ensure much flexibility and allow the joint
modelling of the scale (approval rate) and the shape (uncertainty) of the distribution
of the ranks assigned to the object
