Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given observed circumstances. This article presents an estimation method for modeling the conditional joint distribution of bivariate outcomes based on the distribution regression and factorization methods. This method is considered semiparametric in that it allows for flexible modeling of both the marginal and joint distributions conditional on covariates without imposing global parametric assumptions across the entire distribution. In contrast to existing parametric approaches, our method can accommodate discrete, continuous, or mixed variables, and provides a simple yet effective way to capture distributional dependence structures between bivariate outcomes and covariates. Various simulation results confirm that our method can perform similarly or better in finite samples compared to the alternative methods. In an application to the study of a motor third-party liability insurance portfolio, the proposed method effectively estimates risk measures such as the conditional Value-at-Risk and Expected Shortfall. This result suggests that this semiparametric approach can serve as an alternative in insurance risk management.

了解变量依赖性，特别是在给定一组协变量的情况下得出其统计特性，为实际操作管理（例如给定观察情况的风险分析和决策）提供了数学基础。本文提出了一种基于分布回归和因式分解方法对双变量结果的条件联合分布进行建模的估计方法。该方法被认为是半参数的，因为它允许对协变量条件下的边际分布和联合分布进行灵活建模，而无需在整个分布中强加全局参数假设。与现有的参数方法相比，我们的方法可以适应离散、连续或混合变量，并提供了一种简单而有效的方法来捕获双变量结果和协变量之间的分布依赖结构。各种模拟结果证实，与替代方法相比，我们的方法在有限样本中可以表现相似或更好。在汽车第三方责任保险组合研究的应用中，所提出的方法有效地估计了条件风险价值和预期缺口等风险指标。这一结果表明这种半参数方法可以作为保险风险管理的替代方法。所提出的方法有效地估计了风险度量，例如条件风险价值和预期缺口。这一结果表明这种半参数方法可以作为保险风险管理的替代方法。所提出的方法有效地估计了风险度量，例如条件风险价值和预期缺口。这一结果表明这种半参数方法可以作为保险风险管理的替代方法。