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distribution free (aka non-parametric) Prediction Interval Estimation



I'm looking for an implementation of prediction intervals for the "non-parametric" case, conceptually analogous to the normal parametric case as currently implemented in the Distribution Platform in JMP, as illustrated by the following demo by @julian per the JMP STIPS Course.


I have a good textbook reference for this but the method is almost strictly table-based, with some Fortran code for the nonparametric intervals: 

Gerald Hahn and William Meeker, Statistical Intervals: A Guide for Practitioners 1991, Wiley & Sons


Why ask for such a "nuanced" thing??   


In many situations we are required to use non-parametric methods or otherwise transform the data to normal if the sample data indicates non-normality on the basis of the Shapiro-Wilk Goodness-of-Fit test. This is a procedural requirement for some businesses despite the pros and cons of proceduralizing (since in many cases the normal approximation will work just fine if one looks at the assumptions and the conceptual framework of the interval estimation method or the hypothesis testing method).


Thank you,


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