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

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-10-26 DOI:10.1016/j.spl.2024.110289

Issey Sukeda , Tomonari Sei

引用次数: 0

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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在固定的 Kendall's τ 条件下，弗兰克协程是最小信息协程。

在这项工作中，我们从理论和数值两方面证明了弗兰克协整是固定肯德尔τ（MICK）条件下的最小信息协整。首先，我们解释了 MICK 和 Frank 密度都遵循双曲 Liouville 方程。随后，我们证明满足 Liouville 方程的 copula 密度是唯一的 Frank copula。我们的结果证明，根据熵最大化原则，选择 Frank copula 作为合适的 copula 模型等同于使用 Kendall's τ 作为关于真实分布的唯一可用信息。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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