Question

numpy.average()有一个权重选项，但numpy.std()没有。有没有人有解决方法的建议？

Answer 1

以下简短的“手动计算”怎么样？

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

statsmodels中有一个类可以轻松计算加权统计信息：statsmodels.stats.weightstats.DescrStatsW。

假设这个数据集和权重：

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

您初始化该类（请注意，您必须传递校正因子，此时为delta degrees of freedom）：

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

然后你可以计算：

.mean 加权平均值：

>>> weighted_stats.mean      
1.97196261682243

.std 加权标准差：

>>> weighted_stats.std       
0.21434289609681711

.var 加权差异：

>>> weighted_stats.var       
0.045942877107170932

.std_mean standard error加权平均值：
```
>>> weighted_stats.std_mean  
0.020818822467555047
```
以防您对标准误差与标准差之间的关系感兴趣：标准误差（对于ddof == 0）计算为加权标准差除以总和的平方根权重减1（corresponding source for statsmodels version 0.9 on GitHub）：
```
standard_error = standard_deviation / sqrt(sum(weights) - 1)
```

Answer 3

在numpy / scipy中似乎没有这样的功能，但是有一个ticket提出了这个增加的功能。其中包含Statistics.py，它实现了加权标准偏差。

Answer 4

这里还有一个选择：

np.sqrt(np.cov(values, aweights=weights))

Answer 5

gaborous提出了一个很好的例子：

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)

NumPy中的加权标准差

5 个答案: