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The correct application of Mage's Johnson SB procedure for fitting exposure data

Journal of Exposure Science & Environmental Epidemiology volume 17, pages 499–500 (2007)Cite this article

Flynn (2006) made an excellent review of different methods of applying the Johnson SB distribution, also known as the four-parameter lognormal distribution, to exposure data. He applied the Mage (1980a) percentile solution procedure for estimating SB distribution parameters (Johnson, 1949) and compared it with four other methods for fitting the SB model. However, he concluded that Mage's percentile procedure did not always return values for the four SB parameters, and that “the quantile and method-of-moments fitting procedures may provide performance superior to that of the percentile method.”

For y=(x–Xmin)/(Xmax–x), where x is an exposure variable bounded between a minimum value (Xmin) and a maximum value (Xmax), the SB probability density function p(x) is written as Eq. (1), where μ and σ are the mean and SD of log(y), respectively:

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  1. USEPA (retired) and WHO (retired), Newark, Delaware, USA

    David T Mage

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  1. David T Mage
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Correspondence to David T Mage.

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Mage, D. The correct application of Mage's Johnson SB procedure for fitting exposure data. J Expo Sci Environ Epidemiol 17, 499–500 (2007). https://doi.org/10.1038/sj.jes.7500592

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