Statistics function incorrectly computing median

[Miguel Garcia-Blanco]

> Michael Godfrey ran some calculations using Matlab's quantile function.
>
> We can now compare Matlab's quantile (), R's summary(), and Maxima's
> >> quantile (), with the new quantile.m I had hope to add to octave
> (my quantile() calls discrete_inv()).
>
> Unfortunately, Matlab is an outlier :-(
>

MATLAB seems to have two appropriate functions: quantile.m, prctile.m
Help pages:
http://www.mathworks.com/access/helpdesk/help/toolbox/stats/quantile.html
http://www.mathworks.com/access/helpdesk/help/toolbox/stats/prctile.html
Code:
http://ecco2.jpl.nasa.gov/data1/matlab/stats/prctile.m
As far as I can tell from the help pages, they're essentially the same
except that prctile.m uses percentages instead of probabilities.

A quick look at the code for prctile.m and also running some tests suggests
that MATLAB is using R's method 5, whereas R's default is method 7. (I'm
talking about R's quantile function.)

A Google search comes up with the following user-written quantile.m
functions:
http://home.online.no/~pjacklam/matlab/software/util/statutil/quantile.m
http://www.koders.com/matlab/fidEDEC9319B0EC7E1BCC77A1971511A74F37550100.aspx
https://svnserv.cbs.mpg.de/eeglab/browser/branches/eeglab-devel-5.03/eeglab5.03/functions/quantile.m

A quick look at the code/descriptions and running some tests indicates:
Acklam's quantile uses method 7 (continuous)
Holtsberg's quantile(1) uses method 5 (continuous)
Holtsberg's quantile(2) uses method 6 (continuous)
Holtsberg's quantile(3) uses method 2 (discrete)
Makeig/Finelli's quantile uses method 5 (continuous)

-Miguel