  In this paper, we first describe the generalized notion of Cramer-Rao lower
bound obtained by Naudts (2004) using two families of probability density
functions, the original model and an escort model. We reinterpret the results
in Naudts (2004) from a statistical point of view and obtain some interesting
examples in which this bound is attained. Further we obtain information
inequalities which generalize the classical Bhattacharyya bounds in both
regular and non-regular cases.
