The logit-stable distributions and latent utility scales in categorical data applications

The logit-stable distributions are distributions on the unit interval. They have unconventional shapes, are alternatives to beta distributions for random proportions, arise from an axiomatic derivation based upon latent utility scales, have closed-form probabilities, and greater tail-weight than beta distributions. Logit-stable-binomial distributions are counterparts of beta-binomials; they and logit-stable distributions have properties connected to positive stable laws. As alternatives to beta distributions, they have many potential applications in Applied Probability and related modelling.