What does numpy's percentile function do exactly?

Question

From my understanding, numpy's percentile compute the qth percentiles of the data.

But how does it do exactly?

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Say, given x = np.array([1.3, 1.7, 2.4, 2.8, 3.5, 5.6, 6.6, 7.7, 8.8, 9.9]) (10 floats inside).

if I do np.percentile(x, 100), it gives back 9.9000000000000004.

if I do np.percentile(x, 90), it should returns 8.8, right? But it gives back 8.9100000000000001.

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Why there are such diffs? Are these diffs acceptable?

Answer 1

Since version 1.9.0, Numpy's percentile function has an interpolation parameter which is described in the docs like this:

interpolation : {‘linear’, ‘lower’, ‘higher’, ‘midpoint’, ‘nearest’}
This optional parameter specifies the interpolation method to use, when the desired quantile lies between two data points i and j:

• linear: i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j.
• lower: i.
• higher: j.
• nearest: i or j whichever is nearest.
• midpoint: (i + j) / 2.

It defaults to linear. If you want to get 8.8 from your example, run:

np.percentile(x, 90, interopolation='lower')

Answer 2

From my understanding, the 90%-percentile does not have to be an item from the input array.

From the documentation:

Given a vector V of length N, the q-th percentile of V is the q-th ranked value in a sorted copy of V. The values and distances of the two nearest neighbors as well as the interpolation parameter will determine the percentile if the normalized ranking does not match q exactly. This function is the same as the median if q=50, the same as the minimum if q=0 and the same as the maximum if q=100.

The issue with float representation (which is responsible for the slight difference in np.percentile(x, 100) compared to 9.9) is well known.