A discrete Kumaraswamy distribution for modeling rating and ranking data

Abstract We propose a discrete probability distribution supported on the first k positive integers (k 3), defined in terms of the cumulative distribution function of the continuous two-parameter Kumaraswamy distribution supported on the interval (0, 1). This distribution offers an alternative to existing models, such as the discrete Beta, the Beta-Binomial, and the CUB distributions, for modeling ordinal data, which are ubiquitous in applied disciplines. The key properties of the distribution are explored, with a particular focus on the possible shapes of its probability mass function, moments, pseudo-random simulation, and inferential procedures. Regression models where the response variable follows the proposed discrete Kumaraswamy distribution are also discussed. Analyses of different real data sets, regarding individuals’ perspectives on environmental matters, are provided to practically illustrate the model introduced in this work and assess its ability to fit rating or ranking data.