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I was wondering if there is a way to estimate parameters of Johnson SU distributions parameters with some univariate data.

Nick Cox
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syang
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1 Answers1

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The parameters can be estimated either from the quantiles or from the moments of the distribution. Moments should only be used if the moments are known exactly as a very large sample is needed to give an accurate estimate of higher moments. Both of these methods are relatively complicated algorithms but the references below should be enough to solve your problems.

The paper below details the method for fitting by quantiles:

https://www.jstor.org/stable/2335153?seq=1#metadata_info_tab_contents

This paper details the method for fitting by moments:

https://www.jstor.org/tc/accept?origin=%2Fstable%2Fpdf%2F2346692.pdf

It's also implemented as part of an open-source R package (written in c):

https://cran.r-project.org/web/packages/SuppDists/index.html

And an open-source Matlab package (written in Matlab):

https://uk.mathworks.com/matlabcentral/fileexchange/46123-johnson-curve-toolbox

Nick Cox
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Mike
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    References are welcome and often make excellent comments. What we most value here, though, are explanations. – whuber Dec 14 '18 at 16:15
  • It's great that you most value good answers but in lieu of any answer, it seems perverse to punish the only person who tried. I came across this question when I was trying to answer exactly the same thing, this answer would have really helped me so I thought I'd leave it for others, it seems pointless for me to copy out bits of the paper to explain why the paper is right or try to provide details from of the process when the code is linked right there. – Mike Dec 19 '18 at 10:32
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    I completely agree about the problem of punishing with downvotes, so I have upvoted this post to compensate. You, as the person who researched and offered these links, are initially in far the best position to provide some explanation concerning what they are about, which is why I warmly encourage you (and all who are in a comparable position) to offer explanation in addition to link-only answers. Thank you for your contribution! – whuber Dec 19 '18 at 15:32
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    Thanks, I agree with your point and have added some context. – Mike Jan 03 '19 at 10:50
  • Function eJohnsonSU from ExtDist package also fits Johnson's $S_U$ distribution in R. Another possible option may be the function gamlss from the package gamlss, though I am not sure if it can be made to work for fitting a distribution instead of a more complicated model; another function to look into from the same package is JSU. – Richard Hardy Aug 24 '21 at 10:01