Incrementally calculate sample mean, std, and var.

incrementalstats.py

from __future__ import division

import numbers
import numpy as np

class IncrementalMeanStd(object):
    '''Incremental calculation of sample mean, std, and var.

    Based on http://www.johndcook.com/standard_deviation.html
    '''

    def __init__(self):
        super(IncrementalMeanStd, self).__init__()
        self._mk = 0  # mean_k
        self._mk1 = 0 # mean_{k-1}
        self._sk = 0  # s_k
        self._k = 0   # k

    def _update_mean(self, x):
        '''Update sample mean given new sample x.'''
        if self._k == 1:
            return x
        else:
            return self._mk + (x - self._mk) / self._k

    def _update_var(self, x):
        '''Update sample var given new sample x.'''
        if self._k == 1:
            if isinstance(x, (np.number, numbers.Number)):
                return 0
            elif isinstance(x, np.ndarray):
                return np.zeros_like(x)
        else:
            return self._sk + (x - self._mk1) * (x - self._mk)

    def add(self, x):
        '''Add a new sample and update calculation.'''
        self._k += 1
        self._mk1 = self._mk
        self._mk = self._update_mean(x)
        self._sk = self._update_var(x)

    @property
    def mean(self):
        '''Sample mean.'''
        return self._mk

    @property
    def std(self):
        '''Sample std.'''
        return np.sqrt(self.var)

    @property
    def var(self):
        '''Sample var.'''
        return self._sk / self._k

if __name__ == '__main__':
    # Test
    ims = IncrementalMeanStd()
    l = range(10)
    for x in l:
        ims.add(x)
        print(ims.mean, ims.std, ims.var)