{"title":"相关与非等价伯努利随机变量和的极限定理","authors":"Deepak Singh, Somesh Kumar","doi":"10.1080/01966324.2019.1673266","DOIUrl":null,"url":null,"abstract":"SYNOPTIC ABSTRACT In this paper, a new class of dependent Bernoulli random variables is defined. Here the probability of success at a given trial is a function of the number of successes and probabilities of successes in the previous trials. The moment structure for this model is derived. Further, the strong law of large numbers, the central limit theorem and the law of iterated logarithm are established under a condition that the success probabilities be monotone. Simulations are carried out to demonstrate the law of large numbers and the central limit theorem.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"39 1","pages":"150 - 165"},"PeriodicalIF":0.0000,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2019.1673266","citationCount":"2","resultStr":"{\"title\":\"Limit Theorems for Sums of Dependent and Non-Identical Bernoulli Random Variables\",\"authors\":\"Deepak Singh, Somesh Kumar\",\"doi\":\"10.1080/01966324.2019.1673266\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SYNOPTIC ABSTRACT In this paper, a new class of dependent Bernoulli random variables is defined. Here the probability of success at a given trial is a function of the number of successes and probabilities of successes in the previous trials. The moment structure for this model is derived. Further, the strong law of large numbers, the central limit theorem and the law of iterated logarithm are established under a condition that the success probabilities be monotone. Simulations are carried out to demonstrate the law of large numbers and the central limit theorem.\",\"PeriodicalId\":35850,\"journal\":{\"name\":\"American Journal of Mathematical and Management Sciences\",\"volume\":\"39 1\",\"pages\":\"150 - 165\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/01966324.2019.1673266\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Journal of Mathematical and Management Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/01966324.2019.1673266\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Business, Management and Accounting\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematical and Management Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/01966324.2019.1673266","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Business, Management and Accounting","Score":null,"Total":0}
Limit Theorems for Sums of Dependent and Non-Identical Bernoulli Random Variables
SYNOPTIC ABSTRACT In this paper, a new class of dependent Bernoulli random variables is defined. Here the probability of success at a given trial is a function of the number of successes and probabilities of successes in the previous trials. The moment structure for this model is derived. Further, the strong law of large numbers, the central limit theorem and the law of iterated logarithm are established under a condition that the success probabilities be monotone. Simulations are carried out to demonstrate the law of large numbers and the central limit theorem.
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