I’ve been rewriting a matlab/octave program into numpy and ran across a difference in some resultant values.
This occurs with both the percentile/prctile and the stdard-deviation functions.
In Numpy:
import matplotlib.mlab as ml
import numpy
>>> t = numpy.linspace(0,100, 100)
>>> numpy.percentile(t,95)
95.0
>>> numpy.std(t)
29.157646512850626
>>> ml.prctile(t,95)
95.000000000000014
In Octave:
octave:1> t = linspace(0,100,100)';
octave:2> prctile(t,95)
ans = 95.454545
octave:3> std(t)
ans = 29.304537
Although the array values of ‘t’ are the same, the results are more different than I would suspect.
In the numpy help(numpy.std) they specifically mention that the algorithm is:
std = sqrt(mean(abs(x - x.mean())**2))
So I implemented that in octave and got the exact answer numpy gives. So it seems the std-deviation function differs.
But why/how? And which is correct? (if there is such a thing)
And even prctile/percentile?
Just in case since I’m in Linux aptosid…
GNU Octave, version 3.6.2
numpy.version ‘1.6.2rc1’
Numpy simply uses a different algorithm when the percentile lies between two data points. Octave, Matlab and R always center it exactly between two points when needed (I believe), numpy does a bit more then that… if you check http://en.wikipedia.org/wiki/Percentile you will see there are a couple of ways to calculate percentiles.