Replication Data for: Normal Mode Copulas for Nonmonotonic Dependence

Copulas are helpful in studying joint distributions of two variables, in particular, when confounders are unobserved. However, most conventional copulas cannot model joint distributions where one variable does not increase or decrease in the other in a monotonic manner. For instance, suppose that two variables are linearly positively correlated for one type of unit and negatively for another type of unit. If the type is unobserved, we can observe only a mixture of both types. Seemingly, one variable tends to take either a high or low value (or a middle value) when the other variable is small (large), or vice versa. To address this issue, I consider an overlooked copula with trigonometric functions Chesneau (2021) that I name the \"normal mode copula.\" I apply the copula to a dataset about government formation and duration to demonstrate that the normal mode copula has better performance than other conventional copulas.柯普拉函数（Copula）在研究双变量联合分布领域颇具应用价值，尤其适用于混淆变量未被观测的场景。然而，多数传统柯普拉函数无法对“一变量不随另一变量呈单调增减”的联合分布进行建模。例如，假设存在两类单位：一类中两变量呈线性正相关，另一类则呈线性负相关。若该单位类型未被观测，则仅能观测到两类样本的混合分布。此时直观来看，当其中一变量取较小（或较大）值时，另一变量往往取高值、低值或中间值，反之亦然。为解决这一建模难题，本文采用了Chesneau（2021）提出的一类此前被忽视的三角函数型柯普拉函数，并将其命名为“常态众数柯普拉（normal mode copula）”。随后，本文将该柯普拉函数应用于一则包含政府组建与执政时长信息的数据集，实证结果表明，常态众数柯普拉的建模表现优于其他传统柯普拉函数。