The Johnson System of Frequency Curves—Historical, Graphical, and Limiting Perspectives.
The idea of transforming one random variate to another with a more convenient density has been developed in the first half of the 20th century. In his thesis, Norman L. Johnson (1917–2004) developed a pioneering system of transformations of the standard normal distribution which gained substantial p...
| Published in: | American Statistician Vol. 74; no. 1; pp. 37 - 53 |
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| Main Authors: | , |
| Format: | Article |
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Taylor & Francis Ltd
Feb2020
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| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=141377223&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 141377223 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: Feb2020 vid: 74 iid: 1 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 141377223 10.1080/00031305.2019.1637778 ppf: 37 ppct: 16 formats: tig: atl: The Johnson System of Frequency Curves—Historical, Graphical, and Limiting Perspectives. aug: au: van Dorp, Johan René Jones, M. C. affil: Department of Engineering Management and Systems Engineering, School of Engineering and Applied Science, The George Washington University, Washington, DC School of Mathematics and Statistics, Faculty of STEM, The Open University, Milton Keynes, UK su: Probability density function Kurtosis Geometric series Skewness (Probability theory) Gaussian distribution Frequency curves Twentieth century sug: subj: Probability density function Kurtosis Geometric series Skewness (Probability theory) Gaussian distribution Frequency curves Twentieth century keyword: SB system SL system SU system SB system SL system SU system ab: The idea of transforming one random variate to another with a more convenient density has been developed in the first half of the 20th century. In his thesis, Norman L. Johnson (1917–2004) developed a pioneering system of transformations of the standard normal distribution which gained substantial popularity in the second half of the 20th century and beyond. In Johnson's 1949Biometrika paper entitled Systems of frequency curves generated by methods of translation, summarizing that thesis, one of his primary interests was the behavior of the shape of the probability density functions as their parameter values change. Herein, we attempt to further elucidate this behavior through a series of geometric expositions of that transformation process. In these expositions insight is obtained into the behavior of Johnson's density functions, and their skewness and kurtosis, as they converge to their limiting distributions, a topic which received little attention. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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