Discussion about inaccuracy measure in information theory using co-copula and copula dual functions

Inaccuracy measure is an important measure in information theory, which have been considered recently by many researchers, so that various generalizations have been introduced for this measure. In this paper, two new inaccuracy measures using co-copula and dual of a copula in copula theory are introduced and their properties under specific conditions are investigated. Including, under the establishment of proportional reversed hazard rate model and proportional hazard rate model, we obtain bounds and inequalities for these two inaccuracy measures, and we show that the triangle inequality can also exist for both of these measures. Also, under the assumption of radial symmetry, we prove the equality of these two new inaccuracies. In addition, we obtain a characterization property using the equality of these two inaccuracy measures for radially symmetric distributions. We provide examples to evaluate the results. Finally, in supplementary material section, by introducing estimators for the introduced inaccuracy measures, we examine some of the results using simulation methods and provide an example with real data.