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Created March 21, 2012 19:29
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Python Welford Algorithm
import math
class Welford(object):
""" Implements Welford's algorithm for computing a running mean
and standard deviation as described at:
can take single values or iterables
mean - returns the mean
std - returns the std
meanfull- returns the mean and std of the mean
>>> foo = Welford()
>>> foo(range(100))
>>> foo
<Welford: 49.5 +- 29.0114919759>
>>> foo([1]*1000)
>>> foo
<Welford: 5.40909090909 +- 16.4437417146>
>>> foo.mean
>>> foo.std
>>> foo.meanfull
(5.409090909090906, 0.4957974674244838)
def __init__(self,lst=None):
self.k = 0
self.M = 0
self.S = 0
def update(self,x):
if x is None:
self.k += 1
newM = self.M + (x - self.M)*1./self.k
newS = self.S + (x - self.M)*(x - newM)
self.M, self.S = newM, newS
def consume(self,lst):
lst = iter(lst)
for x in lst:
def __call__(self,x):
if hasattr(x,"__iter__"):
def mean(self):
return self.M
def meanfull(self):
return self.mean, self.std/math.sqrt(self.k)
def std(self):
if self.k==1:
return 0
return math.sqrt(self.S/(self.k-1))
def __repr__(self):
return "<Welford: {} +- {}>".format(self.mean, self.std)
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Beautiful! You'd be surprised at how many incorrect versions of Welford are online, thanks!

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gerardsimons commented Feb 27, 2020

Nice code! One minor thing: not sure if returning an std of 0 is appropriate in the case of k=1 though as this is confusing when k != 0 but std = 0?

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