New Flexible Probability distributions for ranking data

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.