This is a Python implementation of Ted Dunning's t-digest data structure. The t-digest data structure is designed around computing accurate estimates from either streaming data, or distributed data. These estimates are percentiles, quantiles, trimmed means, etc. Two t-digests can be added, making the data structure ideal for map-reduce settings, and can be serialized into much less than 10kB (instead of storing the entire list of data).

See a blog post about it here: Percentile and Quantile Estimation of Big Data: The t-Digest

tdigest is compatible with both Python 2 and Python 3.

pip install tdigest

from tdigest import TDigest
from numpy.random import random

digest = TDigest()
for x in range(5000):
    digest.update(random())

print(digest.percentile(15))  # about 0.15, as 0.15 is the 15th percentile of the Uniform(0,1) distribution

another_digest = TDigest()
another_digest.batch_update(random(5000))
print(another_digest.percentile(15))

sum_digest = digest + another_digest 
sum_digest.percentile(30)  # about 0.3

You can use the to_dict() method to turn a TDigest object into a standard Python dictionary.

digest = TDigest()
digest.update(1)
digest.update(2)
digest.update(3)
print(digest.to_dict())

Or you can get only a list of Centroids with centroids_to_list().

digest.centroids_to_list()

Similarly, you can restore a Python dict of digest values with update_from_dict(). Centroids are merged with any existing ones in the digest. For example, make a fresh digest and restore values from a python dictionary.

digest = TDigest()
digest.update_from_dict({'K': 25, 'delta': 0.01, 'centroids': [{'c': 1.0, 'm': 1.0}, {'c': 1.0, 'm': 2.0}, {'c': 1.0, 'm': 3.0}]})

K and delta values are optional, or you can provide only a list of centroids with update_centroids_from_list().

digest = TDigest()
digest.update_centroids([{'c': 1.0, 'm': 1.0}, {'c': 1.0, 'm': 2.0}, {'c': 1.0, 'm': 3.0}])

If you want to serialize with other tools like JSON, you can first convert to_dict().

json.dumps(digest.to_dict())

Alternatively, make a custom encoder function to provide as default to the standard json module.

def encoder(digest_obj):
    return digest_obj.to_dict()

Then pass the encoder function as the default parameter.

json.dumps(digest, default=encoder)

TDigest.

• update(x, w=1): update the tdigest with value x and weight w.
• batch_update(x, w=1): update the tdigest with values in array x and weight w.
• compress(): perform a compression on the underlying data structure that will shrink the memory footprint of it, without hurting accuracy. Good to perform after adding many values.
• percentile(p): return the pth percentile. Example: p=50 is the median.
• cdf(x): return the CDF the value x is at.
• trimmed_mean(p1, p2): return the mean of data set without the values below and above the p1 and p2 percentile respectively.
• to_dict(): return a Python dictionary of the TDigest and internal Centroid values.
• update_from_dict(dict_values): update from serialized dictionary values into the TDigest object.
• centroids_to_list(): return a Python list of the TDigest object's internal Centroid values.
• update_centroids_from_list(list_values): update Centroids from a python list.