  We address the question and related controversy of the formulation of the
$q$-entropy, and its relative entropy counterpart, for models described by
continuous (non-discrete) sets of variables. We notice that an $L_p$ normalized
functional proposed by Lutwak-Yang-Zhang (LYZ), which is essentially a
variation of a properly normalized relative R\'{e}nyi entropy up to a
logarithm, has extremal properties that make it an attractive candidate which
can be used to construct such a relative $q$-entropy. We comment on the
extremizing probability distributions of this LYZ functional, its relation to
the escort distributions, a generalized Fisher information and the
corresponding Cram\'{e}r-Rao inequality. We point out potential physical
implications of the LYZ entropic functional and of its extremal distributions.
