Aspects of Conditional Symmetry and Asymmetry of Copulas

‎‎The assumption of conditional symmetry‎, ‎which implies that the distribution of one random variable given another random variable has a symmetric form‎, ‎plays a crucial role in various probability and statistics problems‎. ‎This study examines copula properties related to the conditional symmetry/asymmetry of two random variables‎. ‎We investigate the possibility of ordering copulas based on their level of conditional asymmetry‎, ‎similar to the concordance ordering for dependence‎. ‎To quantify the degree of conditional asymmetry of a copula‎, ‎we introduce measures that are monotonic for the proposed ordering‎. ‎The characteristics of the proposed order and measures are elaborated upon‎. ‎Several examples are included to demonstrate the results‎. ‎

کلیدواژه ها:

Asymmetry ، ‎Bivariate symmetry ، ‎ ‎Conditional symmetry ، ‎ ‎Copula‎ ، dependence