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Efficient percentile estimation of streaming or distributed data

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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


Update the digest sequentially

from tdigest import TDigest
from numpy.random import random

digest = TDigest()
for x in range(5000):

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

Update the digest in batches

another_digest = TDigest()

Sum two digests to create a new digest

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

To dict or serializing a digest with JSON

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

digest = TDigest()

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


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)



  • 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.


t-Digest data structure in Python. Useful for percentiles and quantiles, including distributed enviroments like PySpark





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