{"title":"作用于多个多元分布函数的函数","authors":"Paul Ressel","doi":"10.1515/demo-2023-0104","DOIUrl":null,"url":null,"abstract":"Abstract Functions <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> </m:math> f on <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>]</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msup> </m:math> {\\left[0,1]}^{m} such that every composition <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> <m:mrow> <m:mo>∘</m:mo> </m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> f\\circ \\left({g}_{1},\\ldots ,{g}_{m}) with <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>d</m:mi> </m:math> d -dimensional distribution functions <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo form=\"prefix\">,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:math> {g}_{1},\\ldots ,{g}_{m} is again a distribution function, turn out to be characterized by a very natural monotonicity condition, which for <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>d</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> d=2 means ultramodularity. For <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>m</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> m=1 (and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>d</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> d=2 ), this is equivalent with increasing convexity.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"99 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Functions operating on several multivariate distribution functions\",\"authors\":\"Paul Ressel\",\"doi\":\"10.1515/demo-2023-0104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Functions <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>f</m:mi> </m:math> f on <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msup> <m:mrow> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>]</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msup> </m:math> {\\\\left[0,1]}^{m} such that every composition <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>f</m:mi> <m:mrow> <m:mo>∘</m:mo> </m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> f\\\\circ \\\\left({g}_{1},\\\\ldots ,{g}_{m}) with <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>d</m:mi> </m:math> d -dimensional distribution functions <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo form=\\\"prefix\\\">,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:math> {g}_{1},\\\\ldots ,{g}_{m} is again a distribution function, turn out to be characterized by a very natural monotonicity condition, which for <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>d</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> d=2 means ultramodularity. For <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>m</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> m=1 (and <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>d</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> d=2 ), this is equivalent with increasing convexity.\",\"PeriodicalId\":43690,\"journal\":{\"name\":\"Dependence Modeling\",\"volume\":\"99 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dependence Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/demo-2023-0104\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dependence Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/demo-2023-0104","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
摘要
函数f f on [0,1] m {\left[0,1]}^{m}使得f\circ \left({g}_{1}，\ldots，{g}_{m})与d维分布函数g 1，…，g m {g}_{1}，\ldots，{g}_{m}的每一个组合都是一个分布函数，证明它具有一个非常自然的单调性条件，对于d=2, d=2意味着超模性。对于m=1 m=1(和d=2 d=2)，这等同于增加凸性。
Functions operating on several multivariate distribution functions
Abstract Functions f f on [0,1]m {\left[0,1]}^{m} such that every composition f∘(g1,…,gm) f\circ \left({g}_{1},\ldots ,{g}_{m}) with d d -dimensional distribution functions g1,…,gm {g}_{1},\ldots ,{g}_{m} is again a distribution function, turn out to be characterized by a very natural monotonicity condition, which for d=2 d=2 means ultramodularity. For m=1 m=1 (and d=2 d=2 ), this is equivalent with increasing convexity.
期刊介绍：
The journal Dependence Modeling aims at providing a medium for exchanging results and ideas in the area of multivariate dependence modeling. It is an open access fully peer-reviewed journal providing the readers with free, instant, and permanent access to all content worldwide. Dependence Modeling is listed by Web of Science (Emerging Sources Citation Index), Scopus, MathSciNet and Zentralblatt Math. The journal presents different types of articles: -"Research Articles" on fundamental theoretical aspects, as well as on significant applications in science, engineering, economics, finance, insurance and other fields. -"Review Articles" which present the existing literature on the specific topic from new perspectives. -"Interview articles" limited to two papers per year, covering interviews with milestone personalities in the field of Dependence Modeling. The journal topics include (but are not limited to): -Copula methods -Multivariate distributions -Estimation and goodness-of-fit tests -Measures of association -Quantitative risk management -Risk measures and stochastic orders -Time series -Environmental sciences -Computational methods and software -Extreme-value theory -Limit laws -Mass Transportations
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