T-Digest data structure

## Project description

# tdigest
### Efficient percentile estimation of streaming or distributed data
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This is a Python implementation of Ted Dunning's [t-digest](https://github.com/tdunning/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](http://dataorigami.net/blogs/napkin-folding/19055451-percentile-and-quantile-estimation-of-big-data-the-t-digest)

### Installation
*tdigest* is compatible with both Python 2 and Python 3.

```
pip install tdigest
```

### Usage

#### Update the digest sequentially

```
from tdigest import TDigest
from numpy.random import random

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

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

#### Update the digest in batches

```
another_digest = TDigest()
another_digest.batch_update(random(5000))
print another_digest.percentile(0.15)
```

#### Sum two digests to create a new digest

```
sum_digest = digest + another_digest
```

### API

`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(q)`: return the `q`th percentile. Example: `q=.50` is the median.
- `quantile(q)`: return the percentile the value `q` is at.
- `trimmed_mean(q1, q2)`: return the mean of data set without the values below and above the `q1` and `q2` percentile respectively.