Change of Variables theorem to fit Bimodal Distributions

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