Change of Variables theorem to fit Bimodal Distributions

Bimodality is observed in empirical distributions of variables related to materials (glass resistance), companies (productivity) and natural phenomena (geyser eruption). Our proposal for modeling bimodality exploits the change of variables theorem requiring the choice of a generating density function which represents the main features of the phenomena under analysis, and the choice of the transforming function ϕ(x) that describes the observed departure from the expected behaviour. The novelty of this work consists in putting attention to the choice of ϕ(x) in two different cases: when bimodality arises from a slight departure from unimodality and when it is a proper structural feature of the variable under study. As an example we use the R ”geyser” dataset.