用于检验二进制序列等概率的平滑版频谱检验的极限定理

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI:10.1515/dma-2023-0029

M. P. Savelov

{"title":"用于检验二进制序列等概率的平滑版频谱检验的极限定理","authors":"M. P. Savelov","doi":"10.1515/dma-2023-0029","DOIUrl":null,"url":null,"abstract":"Abstract We consider the problem of testing the hypothesis that the tested sequence is a sequence of independent random variables that take values 1 and –1 with equal probability. To solve this problem, the Discrete Fourier Transform (spectral) test of the NIST package uses the statistic TFourier, the exact limiting distribution of which is unknown. In this paper a new statistic is proposed and its limiting distribution is established. This new statistic is a slight modification of TFourier. A hypothesis about the limit distribution of TFourier is formulated, which is confirmed by numerical experiments presented by Pareschi F., Rovatti R. and Setti G.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence\",\"authors\":\"M. P. Savelov\",\"doi\":\"10.1515/dma-2023-0029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We consider the problem of testing the hypothesis that the tested sequence is a sequence of independent random variables that take values 1 and –1 with equal probability. To solve this problem, the Discrete Fourier Transform (spectral) test of the NIST package uses the statistic TFourier, the exact limiting distribution of which is unknown. In this paper a new statistic is proposed and its limiting distribution is established. This new statistic is a slight modification of TFourier. A hypothesis about the limit distribution of TFourier is formulated, which is confirmed by numerical experiments presented by Pareschi F., Rovatti R. and Setti G.\",\"PeriodicalId\":11287,\"journal\":{\"name\":\"Discrete Mathematics and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/dma-2023-0029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2023-0029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

摘要我们考虑的问题是测试这样一个假设，即被测序列是一个独立随机变量序列，其取值 1 和 -1 的概率相等。为了解决这个问题，NIST 软件包中的离散傅立叶变换（频谱）检验使用了统计量 TFourier，但其确切的极限分布是未知的。本文提出了一种新的统计量，并确定了其极限分布。这一新统计量是对 TFourier 统计量的轻微修改。Pareschi F., Rovatti R. 和 Setti G. 提出的数值实验证实了这一假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence

Abstract We consider the problem of testing the hypothesis that the tested sequence is a sequence of independent random variables that take values 1 and –1 with equal probability. To solve this problem, the Discrete Fourier Transform (spectral) test of the NIST package uses the statistic TFourier, the exact limiting distribution of which is unknown. In this paper a new statistic is proposed and its limiting distribution is established. This new statistic is a slight modification of TFourier. A hypothesis about the limit distribution of TFourier is formulated, which is confirmed by numerical experiments presented by Pareschi F., Rovatti R. and Setti G.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.