[proFit-list] Feature request: Quantiles

[Davide Guarisco]

Hello,
	I think that pro Fit should add the calculation of arbitrary  
quantiles to its Statistics capabilities.

Calculating quantiles different from the median or the quartiles  
(which pro Fit already can calculate, or at least display in box  
plots) is sometimes needed in the statistical analysis of data.

A user should be able to:
- turn on the calculation of one or more arbitrary quantiles in the  
Statistics window (perhaps using an interface similar to the one for  
custom graph axis ticks) by entering the desired quantile p (from 0 to  
1, ex. 0.5 for the median), and the quantile type (an integer from 1  
to 9, or more, see below)
- call the Statistics procedure in a program with appropriate new  
parameters and retrieve the result using GetResult

As for the calculation of the quantiles, there exist many different  
methods. I would recommend that pro Fit follows the implementation of  
R, the open-source statistical program (http://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html 
). That is, there are 9 quantile types, with default using type 7.

This is based on the following paper:
Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in statistical  
packages, American Statistician, 50, 361–365.

I have found sample code here:
http://tolstoy.newcastle.edu.au/R/devel/04/07/0180.html

And implemented it as an example in the attached pro Fit program. This  
is given without warranty, however I believe it is correct. I verified  
it with Mathematica using the definitions here:
http://mathworld.wolfram.com/Quantile.html
and some of the canonical data sets below.

For an additional discussion on quantiles, see:
http://www.amstat.org/publications/jse/v14n3/langford.html

Thanks,
       Davide
--
Davide Guarisco

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