  The $\beta$-exponential inflation is driven by a class of primordial
potentials, derived in the framework of braneworld scenarios, that generalizes
the well-known power law inflation. In this paper we update previous
constraints on the minimal coupled $\beta$-exponential model [1] and extend the
results also deriving the equations for the non-minimal coupled scenario. The
predictions of both models are tested in light of the latest temperature and
polarization maps of the Cosmic Microwave Background and clustering data. We
also compare the predictions of these models with the standard $\Lambda$CDM
cosmology using the Deviance Information Criterion (DIC), and find that the
observational data show a moderate preference for the non-minimally coupled
$\beta$-exponential inflationary model.
