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The Johnson System of Frequency Curves—Historical, Graphical, and Limiting Perspectives

van Dorp, Johan René and Jones, M. C. (2020). The Johnson System of Frequency Curves—Historical, Graphical, and Limiting Perspectives. The American Statistician, 74(1) pp. 37–52.

DOI (Digital Object Identifier) Link: https://doi.org/10.1080/00031305.2019.1637778
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Abstract

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 1949 Biometrika 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.

Item Type: Journal Item
Copyright Holders: 2019 American Statistical Association
ISSN: 1537-2731
Keywords: Gaussian distribution
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 66306
SWORD Depositor: Jisc Publications-Router
Depositing User: Jisc Publications-Router
Date Deposited: 29 Aug 2019 11:19
Last Modified: 07 Feb 2020 16:11
URI: http://oro.open.ac.uk/id/eprint/66306
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