  Divergence measures have a long association with statistical inference,
machine learning and information theory. The density power divergence and
related measures have produced many useful (and popular) statistical
procedures, which provide a good balance between model efficiency on one hand
and outlier stability or robustness on the other. The logarithmic density power
divergence, a particular logarithmic transform of the density power divergence,
has also been very successful in producing efficient and stable inference
procedures; in addition it has also led to significant demonstrated
applications in information theory. The success of the minimum divergence
procedures based on the density power divergence and the logarithmic density
power divergence (which also go by the names $\beta$-divergence and
$\gamma$-divergence, respectively) make it imperative and meaningful to look
for other, similar divergences which may be obtained as transforms of the
density power divergence in the same spirit. With this motivation we search for
such transforms of the density power divergence, referred to herein as the
functional density power divergence class. The present article characterizes
this functional density power divergence class, and thus identifies the
available divergence measures within this construct that may be explored
further for possible applications in statistical inference, machine learning
and information theory.
