在固定的 Kendall's τ 条件下，弗兰克协程是最小信息协程。

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

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引用次数: 0

摘要

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。

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

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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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

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.