Generating function for generalized Fisher information measure and its application to finite mixture models

In this work, we consider generating function for generalized Fisher information measure and use it to develop some results for this measure. Next, we study generalized Fisher information for the mixing parameter vector of a finite mixture density function and develop some results for this model. Further, we propose a Jensen-type divergence measure, namely, Jensen-generalized Fisher information (JGFI), and establish some properties for this measure and its generating function. Finally, for illustrative purposes, we examine a real example from image processing and provide some numerical results in terms of JGFI measure.