The Set of Basis Functions Generated by Pearson Type IV Distributions and Its Application to Problems of Statistical Data Analysis and Quantum Mechanics

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI:10.1134/s0081543824010061

Yu. I. Bogdanov, N. A. Bogdanova, V. F. Lukichev

引用次数: 0

Abstract

Using an example of Pearson type IV distributions, we propose a procedure of completing the classical probability distribution to a quantum state. We obtain a wave function corresponding to Pearson type IV distributions and construct the corresponding set of basis functions. Then we demonstrate how the developed method applies to problems of statistical data analysis and quantum mechanics, and show the efficiency of our approach for the problem of approximating statistical distributions with heavy tails.

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皮尔逊 IV 型分布生成的基函数集及其在统计数据分析和量子力学问题中的应用

摘要以皮尔逊 IV 型分布为例，我们提出了一种将经典概率分布补全为量子态的程序。我们获得了与皮尔逊 IV 型分布相对应的波函数，并构建了相应的基函数集。然后，我们演示了所开发的方法如何应用于统计数据分析和量子力学问题，并展示了我们的方法在近似重尾统计分布问题上的效率。

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

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.