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Frank copula is minimum information copula under fixed Kendall’s τ

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  • Sukeda, Issey
  • Sei, Tomonari

Abstract

In this work, we demonstrate that the Frank copula is the minimum information copula under fixed Kendall’s τ (MICK), both theoretically and numerically. First, we explain that both MICK and the Frank density follow the hyperbolic Liouville equation. Subsequently, 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 τ as the sole available information about the true distribution, based on the entropy maximization principle.

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  • Sukeda, Issey & Sei, Tomonari, 2025. "Frank copula is minimum information copula under fixed Kendall’s τ," Statistics & Probability Letters, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:stapro:v:217:y:2025:i:c:s016771522400258x
    DOI: 10.1016/j.spl.2024.110289
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    References listed on IDEAS

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    1. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    2. Tim Bedford & Kevin Wilson, 2014. "On the construction of minimum information bivariate copula families," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 703-723, August.
    3. Kurowicka, Dorota & van Horssen, Wim T., 2015. "On an interaction function for copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 127-142.
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