NumPy中的加權標準偏差？

Question

numpy.average()有一個權重選項，但numpy.std()沒有。有沒有人有解決方法的建議？

Answer 1

以下簡短的「手動計算」如何？

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)) 

Answer 2

在numpy/scipy中似乎還沒有這樣的功能，但是有一個ticket提出了這個附加功能。包括那裏你會發現Statistics.py實施加權標準差。

Answer 3

有在statsmodels一個類來計算加權統計：statsmodels.stats.weightstats.DescrStatsW：

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 

weighted_stats = DescrStatsW(array, weights=weights, ddof=0) 

weighted_stats.mean  # weighted mean of data (equivalent to np.average(array, weights=weights)) 
# 1.97196261682243 

weighted_stats.std  # standard deviation with default degrees of freedom correction 
# 0.21434289609681711 

weighted_stats.std_mean # standard deviation of weighted mean 
# 0.020818822467555047 

weighted_stats.var  # variance with default degrees of freedom correction 
# 0.045942877107170932 

這個類的很好的功能是，如果你想計算不同的統計特性隨後調用將是非常快的，因爲已經計算（甚至中間）的結果被緩存。

Answer 4

有由gaborous提出了一個很好的例子：

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)