Abstract
Abstract
The purpose of this paper is twofold. The first part is to introduce relative-
$\chi_{\alpha}^{2}$
, Jensen-
$\chi_{\alpha}^{2}$
and (p, w)-Jensen-
$\chi_{\alpha}^2$
divergence measures and then examine their properties. In addition, we also explore possible connections between these divergence measures and Jensen–Shannon entropy measure. In the second part, we introduce
$(p,\eta)$
-mixture model and then show it to be an optimal solution to three different optimization problems based on
$\chi_{\alpha}^{2}$
divergence measure. We further study the relative-
$\chi_{\alpha}^{2}$
divergence measure for escort and arithmetic mixture densities. We also provide some results associated with relative-
$\chi_{\alpha}^{2}$
divergence measure of mixed reliability systems. Finally, to demonstrate the usefulness of the Jensen-
$\chi_{\alpha}^{2}$
divergence measure, we apply it to a real example in image processing and present some numerical results. Our findings in this regard show that the Jensen-
$\chi_{\alpha}^{2}$
is an effective criteria for quantifying the similarity between two images.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability