  When scholars study joint distributions of multiple variables, copulas are
useful. However, if the variables are not linearly correlated with each other
yet are still not independent, most of conventional copulas are not up to the
task. Examples include (inversed) U-shaped relationships and
heteroskedasticity. To fill this gap, this manuscript sheds new light on a
little-known copula, which I call the "normal mode copula." I characterize the
copula's properties and show that the copula is asymmetric and nonmonotonic
under certain conditions. I also apply the copula to a dataset about U.S. House
vote share and campaign expenditure to demonstrate that the normal mode copula
has better performance than other conventional copulas.
