Fréchet–Shohat theorem: Stronger modes of convergence for a class of absolutely continuous distributions

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-06-06 DOI:10.1016/j.spl.2025.110466

Pier Luigi Novi Inverardi, Aldo Tagliani

引用次数: 0

Abstract

Using recent results from information theory, maximum entropy (briefly, MaxEnt) and convergence in entropy of MaxEnt densities, stronger modes of convergence than convergence in distribution are obtained for absolutely continuous distributions. As a first result, an alternative proof of the Fréchet–Shohat theorem is given. Moreover, due to the flexibility of the MaxEnt entropy formalism, the new proof is valid for Hamburger, Stieltjes and Hausdorff moment problems with support

R

R^{+}

[0, 1]

, respectively.

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frsamet - shohat定理：一类绝对连续分布的强收敛模式

利用信息论、最大熵（MaxEnt）和MaxEnt密度的熵收敛的最新结果，得到了绝对连续分布比分布收敛更强的收敛模式。作为第一个结果，给出了frsamet - shohat定理的另一种证明。此外，由于MaxEnt熵形式主义的灵活性，新的证明分别适用于支持度为R、R+、[0,1]的Hamburger、Stieltjes和Hausdorff矩问题。

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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