文章基本信息

标题：THE THEORY OF THE INTERNALLY STUDENTIZED RANGE DISTRIBUTION REVISITED
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作者：Daniel Furtado FERREIRA ; Lucas Monteiro CHAVES ; Devanil Jaques de SOUZA 等
期刊名称：Revista Brasileira de Biometria
印刷版ISSN：0102-0811
电子版ISSN：1983-0823
出版年度：2018
卷号：36
期号：4
页码：802-826
DOI：10.28951/rbb.v36i4.308
出版社：Universidade Federal de Lavras
摘要：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.
关键词：Order statistics; closest of three; normal distribution; uniform distribution.