{"title":"Estimates of the Rates of Convergence in Limit Theorems for the First Passage Times of Random Walks","authors":"D. P. Kennedy","doi":"10.1214/AOMS/1177690890","DOIUrl":"https://doi.org/10.1214/AOMS/1177690890","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"1 1","pages":"2090-2094"},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77325774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of partitioning a set of normal populations with respect to one control has been considered by Tong (1969). This note points at the possibility of using two controls which gives a partitioning into three disjoint groups. The procedure utilizes Tong's tables. It is also stated that the procedure can be used for mixed randomized block designs with a certain symmetry. An extension to more than two controls is also mentioned.
{"title":"A Note on Partitioning a Set of Normal Populations by Their Locations with Respect to Two Controls","authors":"P. Seeger","doi":"10.1214/AOMS/1177690876","DOIUrl":"https://doi.org/10.1214/AOMS/1177690876","url":null,"abstract":"The problem of partitioning a set of normal populations with respect to one control has been considered by Tong (1969). This note points at the possibility of using two controls which gives a partitioning into three disjoint groups. The procedure utilizes Tong's tables. It is also stated that the procedure can be used for mixed randomized block designs with a certain symmetry. An extension to more than two controls is also mentioned.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"178 1","pages":"2019-2023"},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79950780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a Certain Class of Limit Distributions","authors":"R. Shantaram, W. Harkness","doi":"10.1214/AOMS/1177690886","DOIUrl":"https://doi.org/10.1214/AOMS/1177690886","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"37 1","pages":"2067-2071"},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82294561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Inequalities for the Law of Large Numbers","authors":"T. Kurtz","doi":"10.1214/AOMS/1177690858","DOIUrl":"https://doi.org/10.1214/AOMS/1177690858","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"3 1","pages":"1874-1883"},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90069795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Correlation Coefficient of a Bivariate, Equal Variance, Complex Gaussian Sample","authors":"T. Berger","doi":"10.1214/AOMS/1177690873","DOIUrl":"https://doi.org/10.1214/AOMS/1177690873","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"2016 1","pages":"2000-2003"},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86155726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Cramer Von-Mises Type Statistic for Testing Symmetry","authors":"E. Rothman, M. Woodroofe","doi":"10.1214/AOMS/1177690879","DOIUrl":"https://doi.org/10.1214/AOMS/1177690879","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"54 1","pages":"2035-2038"},"PeriodicalIF":0.0,"publicationDate":"1972-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86514085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Asymptotic Expansion for the Distribution of the Eigenvalues of a 3 by 3 Wishart Matrix","authors":"Christopher Bingham","doi":"10.1214/AOMS/1177692382","DOIUrl":"https://doi.org/10.1214/AOMS/1177692382","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"2 1","pages":"1498-1506"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73794832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, confidence bounds on the reliability of a serial system composed of exponential subsystems are considered. Both the classical and the Bayesian analyses are discussed. The main result is that for the case in which there are no previous data, then there are no prior distributions on the subsystem reliabilities that are independent of current data and that yield the uniformly most accurate unbiased confidence bounds available through classical techniques.
{"title":"Bayesian Prior Distributions for Systems with Exponential Failure-time Data","authors":"K. Fertig","doi":"10.1214/AOMS/1177692376","DOIUrl":"https://doi.org/10.1214/AOMS/1177692376","url":null,"abstract":"In this paper, confidence bounds on the reliability of a serial system composed of exponential subsystems are considered. Both the classical and the Bayesian analyses are discussed. The main result is that for the case in which there are no previous data, then there are no prior distributions on the subsystem reliabilities that are independent of current data and that yield the uniformly most accurate unbiased confidence bounds available through classical techniques.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"1 1","pages":"1441-1448"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80142413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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