Single-pass online statistics.
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README.md
test_online_stat.ipynb

README.md

Single-Pass Online Statistics Algorithms

Suppliment to the article:

Single-Pass Online Statistics Algorithms, by Nikolai Shokhirev, 2013

Author

Nikolai Shokhirev

File structure & description

online_statatistics/
    __init__.py
    online_stat.py - Defined: WindowedStat, CumulativeStat, WindowedCovariance, CumulativeCovariance
test/
    __init__.py
    test_utils.py - Defined: win_moment, cum_moment, win_cov, cum_cov
doc/
    online_statistics.html - Generated from notebook: all classes, functions and tests.
README.md
test_online_stat.ipynb - Test/Demo

Dependencies

numpy

API

WindowedStat
    rest(n) - can be called to reuse existing object.
    s - sum
    s2 - central 2-nd order sum
    s3 - central 3-rd order sum
    s4 - central 4-th order sum
    m - mean
    m2 - central 2-nd order moment
    m3 - central 3-rd order moment
    m4 - central 4-th order moment
    
CumulativeStat
    rest() - can be called to reuse existing object.
    Same as above.
    
WindowedCovariance
    rest(n) - can be called to reuse existing object.
    sx - x-sum
    sy - y-sum
    sxy - xy-sum
    mx - x-mean
    my - y-mean
    cov - covarianxe
    
CumulativeCovariance
    rest() - can be called to reuse existing object.
    Same as above.

Usage example

# Test data
X = np.array([0.2,1.0,1.4,2.0,2.7,3.8,5.4,7.5,11,15],dtype=float)
    # Create processing object
    n = 3 # window size
    ws =  = WindowedStat(n)    
    print('Mean,  M2,  M3,  M4')
    for x in X:
        ws.push(x)
        print(ws.m, ws.m2, ws.m3, ws.m4)

Output:

Mean,       M2,  M3,  M4
0.2           0.0 0.0 0.0
0.6           0.16            1.38777878e-17  0.0256
0.86666666667 0.248888888889 -0.0474074074074 0.0929185185185
1.46666666667 0.168888888889  0.0165925925926 0.0427851851852
2.03333333333 0.282222222222  0.0140740740741 0.119474074074
2.83333333333 0.548888888889  0.107407407407  0.451918518519
3.96666666667 1.22888888889   0.302592592593  2.26525185185
5.56666666667 2.29555555556   0.569259259259  7.90436296296
7.96666666667 5.33555555556   3.63325925926 42.7022296296
11.1666666667 9.38888888889   2.34259259259 132.226851852

cs = CumulativeStat()

sSimilar with the other objects.

Test / Demo

test_online_stat.ipynb

License

(The MIT License)

Copyright (c) 2014 Bill Gooch

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the 'Software'), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be

included in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND,
    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF

MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.