  The behaviour of many dynamic real phenomena shows different phases, with
each one following a sigmoidal type pattern. This requires studying sigmoidal
curves with more than one inflection point. In this work, a diffusion process
is introduced whose mean function is a curve of this type, concretely a
transformation of the well-known Gompertz model after introducing in its
expression a polynomial term. The maximum likelihood estimation of the
parameters of the model is studied, and various criteria are provided for the
selection of the degree of the polynomial when real situations are addressed.
Finally, some simulated examples are presented.
