Bounds of Some Divergence Measures Using Hermite Polynomial via Diamond Integrals on Time Scales

Abstract

In this article, an inequality which contains bound of Csiszár divergence is generalised via diamond integral on time scales by utilizing the Hermite polynomial. Various constraints of Hermite polynomial are employed to provide some improvements of this new inequality. Bounds of different divergence measures are obtained by using particular convex functions. Furthermore, in seek of applications in mathematical statistics, bounds of different divergence measures are estimated on diverse fixed time scales. The paper addresses new results which are generalized (unified) form of both discrete and continuous results in literature (As time scales calculus unifies both discrete and continuous cases). Moreover, diamond integral can be used to study hybrid discrete-continuous systems.