Optimal information, Jensen-RIG function and α-Onicescu's correlation coefficient in terms of information generating functions

The purpose of this work is two-fold. The first part is to introduce Jensen-relative information generating function and examine its connection to Jensen–Shannon entropy measure. Then, the α-mixture distribution is shown to be an optimal solution to three optimization problems based on relative information generating (RIG) function. We further study the information generating (IG) and RIG measures for this mixture model. In the second part, we express α-Onicescu's correlation coefficient in terms of information generating function and study it for escort distributions. Finally, we provide some illustrative examples and describe a real application for proposed α-Onicescu's correlation coefficient.