New Flexible Probability Distributions for Ranking Data

Recently, several models have been proposed for analysing the ranks assigned by people to some object. These models summarize the liking feeling towards the object, possibly 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 considered for taking into account the uncertainty in the ranking process. We propose two new probability distributions, the Discrete Beta and the Shifted- Beta Binomial, which ensure much flexibility and allow the joint modelling of the scale (approval rate) and the shape (uncertainty) parameters of the rank distribution.