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Article ID: KB0075272
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Description
Statistica use two methods for calculating Johnson Fit Curves - using the method of moments (default option), and using the percentile method. The 'JohnsonFromMoments' provides the Probability Density Function (PDF) value for a given x, that is, it computes f(x) where f is the JohnsonDistribution specified by the given moments. The vJohnson is the inverse cumulative Johnson or quantile function for the Johnson distribution specified by the given moments (it provides the x for a given F(x) where F is the Cumulative Distribution Function (CDF) of the specified Johnson distribution).
Issue/Introduction
This article details how Statistica calculates Johnson Fit Curves
Resolution
- By default, Johnson Curves in Statistica are fit via the method of moments (which is described in further detail here: https://rss.onlinelibrary.wiley.com/doi/10.2307/2346692 Hill, I. D., Hill, R., & Holder, R. L. (1976) - Fitting Johnson curves by moments. Applied Statistics. 25, 190-192).
- There is a second method that can be used, which is the percentile method ( described in further detail here: Transforming non-normal data to normality in statistical process control. Journal of Quality Technology, 30(2), 133-141 Reference: https://www.tandfonline.com/doi/abs/10.1080/00224065.1998.11979832)
Also, using Statistica Visual Basic (SVB), you can fit via moments by using 'FitJohnsonFromMoments'