In this paper, we aimed to investigate the relationship between energy consumption and carbon dioxide (CO₂) emission quantities. To explain the dependence structure, we employed asymmetric Archimedean copulas and determined the best fitting multi-parameter Archimedean copula based on the λ–function. A goodness-of-fit improvement can be obtained by using concordance invariant and tail dependence preserving transforms. The association of CO₂ emission quantities and energy consumption is characterized by the transformed convex sum of the Gumbel and Clayton copula, indicating evidence of joint extreme occurrences when both of the variables increase or decrease in the industrial sector. Also, the Kendall hazard scenario approach was used to evaluate the probability of extreme events. The results provide valuable information for researchers who model changes in CO₂ emission quantities with energy consumption.

在本文中，我们旨在研究能耗与二氧化碳（CO ₂）排放量之间的关系。为了解释依赖性结构，我们使用了不对称的阿基米德copulas，并基于λ函数确定了最合适的多参数阿基米德copula。通过使用一致性不变和尾部相关性保留变换，可以获得拟合优度的提高。CO ₂的缔合排放量和能源消耗的特征在于Gumbel和Clayton copula的变换凸和，表明当两个变量在工业部门中都增加或减少时，联合出现极端事件的证据。同样，使用肯德尔（Kendall）危险情景方法来评估极端事件的可能性。这些结果为研究人员根据能源消耗模拟CO ₂排放量变化提供了有价值的信息。