NumPy percentile function different from MATLAB's percentile function

matlab, numpy, percentile, python, r

Solution

MATLAB apparently uses midpoint interpolation by default. NumPy and R use linear interpolation by default:

In [182]: np.percentile(x, 75, interpolation='linear')
Out[182]: 11.312249999999999

In [183]: np.percentile(x, 75, interpolation='midpoint')
Out[183]: 11.3165

The understand the difference between `linear` and `midpoint`, consider this simple example:

In [187]: np.percentile([0, 100], 75, interpolation='linear')
Out[187]: 75.0

In [188]: np.percentile([0, 100], 75, interpolation='midpoint')
Out[188]: 50.0

To compile the latest version of NumPy (using Ubuntu):

mkdir $HOME/src
git clone https://github.com/numpy/numpy.git
git remote add upstream https://github.com/numpy/numpy.git
# Read ~/src/numpy/INSTALL.txt
sudo apt-get install libatlas-base-dev libatlas3gf-base
python setup.py build --fcompiler=gnu95
python setup.py install

The advantage of using `git` instead of `pip` is that it is super easy to upgrade (or downgrade) to other versions of NumPy (and you get the source code too):

git fetch upstream
git checkout master # or checkout any other version of NumPy
cd ~/src/numpy
/bin/rm -rf build
cdsitepackages    # assuming you are using virtualenv; otherwise cd to your local python sitepackages directory
/bin/rm -rf numpy numpy-*-py2.7.egg-info
cd ~/src/numpy
python setup.py build --fcompiler=gnu95
python setup.py install

Problem

When I try to calculate the 75th percentile in MATLAB, I get a different value than I do in NumPy. MATLAB: ``` >> x = [ 11.308 ; 7.2896; 7.548 ; 11.325 ; 5.7822; 9.6343; 7.7117; 7.3341; 10.398 ; 6.9675; 10.607 ; 13.125 ; 7.819 ; 8.649 ; 8.3106; 12.129 ; 12.406 ; 10.935 ; 12.544 ; 8.177 ] >> prctile(x, 75) ans = 11.3165 ``` Python + NumPy: ``` >>> import numpy as np >>> x = np.array([ 11.308 , 7.2896, 7.548 , 11.325 , 5.7822, 9.6343, 7.7117, 7.3341, 10.398 , 6.9675, 10.607 , 13.125 , 7.819 , 8.649 , 8.3106, 12.129 , 12.406 , 10.935 , 12.544 , 8.177 ]) >>> np.percentile(x, 75) 11.312249999999999 ``` I've checked the answer with R too, and I'm getting NumPy's answer. R: ``` > x <- c(11.308 , 7.2896, 7.548 , 11.325 , 5.7822, 9.6343, + 7.7117, 7.3341, 10.398 , 6.9675, 10.607 , 13.125 , + 7.819 , 8.649 , 8.3106, 12.129 , 12.406 , 10.935 , + 12.544 , 8.177) > quantile(x, 0.75) 75% 11.31225 ``` What is going on here? And is there any way to make Python & R's behavior mirror MATLAB's?

Original source