问题
numpy.average()
has a weights option, but numpy.std()
does not. Does anyone have suggestions for a workaround?
回答1:
How about the following short "manual calculation"?
def weighted_avg_and_std(values, weights):
"""
Return the weighted average and standard deviation.
values, weights -- Numpy ndarrays with the same shape.
"""
average = numpy.average(values, weights=weights)
# Fast and numerically precise:
variance = numpy.average((values-average)**2, weights=weights)
return (average, math.sqrt(variance))
回答2:
There is a class in statsmodels that makes it easy to calculate weighted statistics: statsmodels.stats.weightstats.DescrStatsW.
Assuming this dataset and weights:
import numpy as np
from statsmodels.stats.weightstats import DescrStatsW
array = np.array([1,2,1,2,1,2,1,3])
weights = np.ones_like(array)
weights[3] = 100
You initialize the class (note that you have to pass in the correction factor, the delta degrees of freedom at this point):
weighted_stats = DescrStatsW(array, weights=weights, ddof=0)
Then you can calculate:
.mean the weighted mean:
>>> weighted_stats.mean 1.97196261682243
.std the weighted standard deviation:
>>> weighted_stats.std 0.21434289609681711
.var the weighted variance:
>>> weighted_stats.var 0.045942877107170932
.std_mean the standard error of weighted mean:
>>> weighted_stats.std_mean 0.020818822467555047
Just in case you're interested in the relation between the standard error and the standard deviation: The standard error is (for
ddof == 0
) calculated as the weighted standard deviation divided by the square root of the sum of the weights minus 1 (corresponding source for statsmodels version 0.9 on GitHub):standard_error = standard_deviation / sqrt(sum(weights) - 1)
回答3:
Here's one more option:
np.sqrt(np.cov(values, aweights=weights))
回答4:
There doesn't appear to be such a function in numpy/scipy yet, but there is a ticket proposing this added functionality. Included there you will find Statistics.py which implements weighted standard deviations.
回答5:
There is a very good example proposed by gaborous:
import pandas as pd
import numpy as np
# X is the dataset, as a Pandas' DataFrame
mean = mean = np.ma.average(X, axis=0, weights=weights) # Computing the
weighted sample mean (fast, efficient and precise)
# Convert to a Pandas' Series (it's just aesthetic and more
# ergonomic; no difference in computed values)
mean = pd.Series(mean, index=list(X.keys()))
xm = X-mean # xm = X diff to mean
xm = xm.fillna(0) # fill NaN with 0 (because anyway a variance of 0 is
just void, but at least it keeps the other covariance's values computed
correctly))
sigma2 = 1./(w.sum()-1) * xm.mul(w, axis=0).T.dot(xm); # Compute the
unbiased weighted sample covariance
Correct equation for weighted unbiased sample covariance, URL (version: 2016-06-28)
来源:https://stackoverflow.com/questions/2413522/weighted-standard-deviation-in-numpy