Generate mu, sigma for a stream of numbers, incrementally.

running.py

import collections


class RunningAverage(object):
    """
    >>> r = RunningAverage()
    >>> r
    <__main__.RunningAverage object at 0x...>
    >>> r.update(1)
    >>> r.update(2)
    >>> r.update(3)
    >>> r.stats()
    (2.0, 0.816...)
    >>> RunningAverage.q((1, 2, 3))
    (2.0, 0.816...)
    >>> RunningAverage.q((1, 2, 3, 6, 10, 12))
    (5.666..., 4.109...)
    """
    def __init__(self):
        self._n = 0
        self._sumx = 0
        self._sumxsq = 0

    def update(self, x):
        def update_one(x):
            self._n += 1
            self._sumx += x
            self._sumxsq += x * x

        if isinstance(x, collections.Iterable):
            [update_one(y) for y in x]
        else:
            update_one(x)

    def stats(self):
        mu = 1.0 * self._sumx / self._n
        sigma = ((1.0 * self._sumxsq / self._n) - mu ** 2) ** 0.5
        return (mu, sigma)

    @classmethod
    def q(cls, lst):
        R = RunningAverage()
        R.update(lst)
        return R.stats()


if __name__ == "__main__":
    import doctest
    doctest.testmod(optionflags=doctest.ELLIPSIS)