  In dependence modeling, various copulas have been utilized. Among them, the
Frank copula has been one of the most typical choices due to its simplicity. In
this work, we demonstrate that the Frank copula is the minimum information
copula under fixed Kendall's $\tau$ (MICK), both theoretically and numerically.
First, we explain that both MICK and the Frank density follow the hyperbolic
Liouville equation. Moreover, we show that the copula density satisfying the
Liouville equation is uniquely the Frank copula. Our result asserts that
selecting the Frank copula as an appropriate copula model is equivalent to
using Kendall's $\tau$ as the sole available information about the true
distribution, based on the entropy maximization principle.
