Optimal probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution nonparametrically over a given broad model class and proving asymptotic efficiency in that setting. The ideas are demonstrated within the context of...

A general class of probability distributions is proposed and its properties examined. The proposed family contains distributions of a wide variety of shapes, such as U shaped, uniform and long-tailed distributions, as well as distributions with supports that have finite limits at one or both...