{"title":"零峰度系数对称分布双组分混合模型的分类","authors":"A.I. Krasilnikov","doi":"10.15407/emodel.45.05.020","DOIUrl":null,"url":null,"abstract":"On the basis of a family of two-component mixtures of distributions, a class K of symmetric non-Gaussian distributions with a zero kurtosis coefficient is defined, which is divided into two groups and five types. The dependence of the fourth-order cumulant on the weight coefficient of the mixture is studied, as a result of which the conditions are determined under which the kurtosis coefficient of the mixture is equal to zero. The use of a two-component mixture of Subbotin distributions for modeling single-vertex symmetric distributions with a zero kurtosis coefficient is justified. Examples of symmetric non-Gaussian distributions with zero kurtosis coefficient are given. The use of class K models gives a practical opportunity at the design stage to compare the effectiveness of the developed methods and systems for non-Gaussian signals with zero coefficients of asymmetry and kurtosis processing.","PeriodicalId":474184,"journal":{"name":"Èlektronnoe modelirovanie","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classification of Models of Two-component Mixtures of Symmetrical Distributions with Zero Kurtosis Coefficient\",\"authors\":\"A.I. Krasilnikov\",\"doi\":\"10.15407/emodel.45.05.020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"On the basis of a family of two-component mixtures of distributions, a class K of symmetric non-Gaussian distributions with a zero kurtosis coefficient is defined, which is divided into two groups and five types. The dependence of the fourth-order cumulant on the weight coefficient of the mixture is studied, as a result of which the conditions are determined under which the kurtosis coefficient of the mixture is equal to zero. The use of a two-component mixture of Subbotin distributions for modeling single-vertex symmetric distributions with a zero kurtosis coefficient is justified. Examples of symmetric non-Gaussian distributions with zero kurtosis coefficient are given. The use of class K models gives a practical opportunity at the design stage to compare the effectiveness of the developed methods and systems for non-Gaussian signals with zero coefficients of asymmetry and kurtosis processing.\",\"PeriodicalId\":474184,\"journal\":{\"name\":\"Èlektronnoe modelirovanie\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Èlektronnoe modelirovanie\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15407/emodel.45.05.020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Èlektronnoe modelirovanie","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15407/emodel.45.05.020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Classification of Models of Two-component Mixtures of Symmetrical Distributions with Zero Kurtosis Coefficient
On the basis of a family of two-component mixtures of distributions, a class K of symmetric non-Gaussian distributions with a zero kurtosis coefficient is defined, which is divided into two groups and five types. The dependence of the fourth-order cumulant on the weight coefficient of the mixture is studied, as a result of which the conditions are determined under which the kurtosis coefficient of the mixture is equal to zero. The use of a two-component mixture of Subbotin distributions for modeling single-vertex symmetric distributions with a zero kurtosis coefficient is justified. Examples of symmetric non-Gaussian distributions with zero kurtosis coefficient are given. The use of class K models gives a practical opportunity at the design stage to compare the effectiveness of the developed methods and systems for non-Gaussian signals with zero coefficients of asymmetry and kurtosis processing.