D. F. Ferreira, L. Chaves, Devanil Jaques de Souza
{"title":"重新审视了内部研究的范围分布理论","authors":"D. F. Ferreira, L. Chaves, Devanil Jaques de Souza","doi":"10.28951/RBB.V36I4.308","DOIUrl":null,"url":null,"abstract":"The present paper intends to revisit the distribution of the ratio of the range to the sample standard deviation, known as the distribution of the internally studentized range, in the normal case. This distribution has its importance recognized in several areas, as quality control and inference, for testing the lack of homogeneity of the data or kurtosis. An alternative distribution to the one presented by David et al. (1954), based on the distribution of the maximum, is proposed. We exhibit a detailed proof for the distribution of the internally studentized range in the normal case and sample size 3. We also provide a new result: the distribution for the uniform case with sample of size 3.","PeriodicalId":36293,"journal":{"name":"Revista Brasileira de Biometria","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"THE THEORY OF THE INTERNALLY STUDENTIZED RANGE DISTRIBUTION REVISITED\",\"authors\":\"D. F. Ferreira, L. Chaves, Devanil Jaques de Souza\",\"doi\":\"10.28951/RBB.V36I4.308\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The present paper intends to revisit the distribution of the ratio of the range to the sample standard deviation, known as the distribution of the internally studentized range, in the normal case. This distribution has its importance recognized in several areas, as quality control and inference, for testing the lack of homogeneity of the data or kurtosis. An alternative distribution to the one presented by David et al. (1954), based on the distribution of the maximum, is proposed. We exhibit a detailed proof for the distribution of the internally studentized range in the normal case and sample size 3. We also provide a new result: the distribution for the uniform case with sample of size 3.\",\"PeriodicalId\":36293,\"journal\":{\"name\":\"Revista Brasileira de Biometria\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Brasileira de Biometria\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.28951/RBB.V36I4.308\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Medicine\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Brasileira de Biometria","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.28951/RBB.V36I4.308","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Medicine","Score":null,"Total":0}
引用次数: 0
摘要
本文打算重新审视在正常情况下，范围与样本标准差之比的分布，即内部研究范围的分布。这种分布的重要性在几个领域得到了认可，如质量控制和推理，用于测试数据的缺乏同质性或峰度。David et al.(1954)提出了一种基于最大值分布的替代分布。我们展示了在正常情况和样本容量3下内部研究范围分布的详细证明。我们还提供了一个新的结果:样本大小为3的均匀情况下的分布。
THE THEORY OF THE INTERNALLY STUDENTIZED RANGE DISTRIBUTION REVISITED
The present paper intends to revisit the distribution of the ratio of the range to the sample standard deviation, known as the distribution of the internally studentized range, in the normal case. This distribution has its importance recognized in several areas, as quality control and inference, for testing the lack of homogeneity of the data or kurtosis. An alternative distribution to the one presented by David et al. (1954), based on the distribution of the maximum, is proposed. We exhibit a detailed proof for the distribution of the internally studentized range in the normal case and sample size 3. We also provide a new result: the distribution for the uniform case with sample of size 3.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
