In the context of additive or multiplicative damage models, and under mild conditions, it is shown that the functional forms of suitably chosen regressions on a random variable X or/and its recorded part Y are characteristic of the distribution of X. The paper treats the cases where the recorded...

An overview of the evolution of probability models for over-dispersion is given looking at their origins, motivation, first main contributions, important milestones and applications. A specific class of models called the Waring and generalized Waring models will be a focal point. Their...