{"title":"Generation of Records Obtained from Sequences of Independent and Non-Identically Distributed Variables","authors":"S. A. Petukhov, A. V. Stepanov","doi":"10.1134/s1063454123040131","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Generation algorithms of record times and values obtained from sequences of independent and non-identically distributed random variables, the distribution functions of which are defined on a common support, are proposed in the present paper. Known algorithms of generation of record times and values are given in Introduction for the case when the initial random variables are independent and identically distributed. A brief review of the scientific literature associated with this topic is also given in Introduction. It is also pointed out there that all efficient algorithms of record generation are based on the Markov property of records. In Section 2, the distribution functions of record times and values are derived for the case when the initial random variables are independent and non-identically distributed. The corresponding record-generation algorithms are proposed for the first time. These algorithms are based on the derived distributions and the Markov property of records, which also holds in the case when the initial observations are independent but non-identically distributed. At the end of this work, in Section 3, the proposed algorithms are tested by simulation experiments. In these experiments the records are generated for the case when the initial random variables have Gumbel distribution functions.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454123040131","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Generation algorithms of record times and values obtained from sequences of independent and non-identically distributed random variables, the distribution functions of which are defined on a common support, are proposed in the present paper. Known algorithms of generation of record times and values are given in Introduction for the case when the initial random variables are independent and identically distributed. A brief review of the scientific literature associated with this topic is also given in Introduction. It is also pointed out there that all efficient algorithms of record generation are based on the Markov property of records. In Section 2, the distribution functions of record times and values are derived for the case when the initial random variables are independent and non-identically distributed. The corresponding record-generation algorithms are proposed for the first time. These algorithms are based on the derived distributions and the Markov property of records, which also holds in the case when the initial observations are independent but non-identically distributed. At the end of this work, in Section 3, the proposed algorithms are tested by simulation experiments. In these experiments the records are generated for the case when the initial random variables have Gumbel distribution functions.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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