python - numpy.cov() 函数是如何实现的？

Question

我有自己的基于等式的协方差函数的实现:

'''
Calculate the covariance coefficient between two variables.
'''

import numpy as np

X = np.array([171, 184, 210, 198, 166, 167])
Y = np.array([78, 77, 98, 110, 80, 69])

# Expected value function.
def E(X, P):
    expectedValue = 0
    for i in np.arange(0, np.size(X)):
        expectedValue += X[i] * (P[i] / np.size(X))
    return expectedValue 

# Covariance coefficient function.
def covariance(X, Y):
    '''
    Calculate the product of the multiplication for each pair of variables
    values.
    '''
    XY = X * Y

    # Calculate the expected values for each variable and for the XY.
    EX = E(X, np.ones(np.size(X)))
    EY = E(Y, np.ones(np.size(Y)))
    EXY = E(XY, np.ones(np.size(XY)))

    # Calculate the covariance coefficient.
    return EXY - (EX * EY)

# Display matrix of the covariance coefficient values.
covMatrix = np.array([[covariance(X, X), covariance(X, Y)], 
[covariance(Y, X), covariance(Y, Y)]])  
print("My function:", covMatrix)

# Display standard numpy.cov() covariance coefficient matrix.
print("Numpy.cov() function:", np.cov([X, Y]))

但问题是，我从我的函数和 numpy.cov() 中得到了不同的值，即:

My function: [[ 273.88888889  190.61111111]
 [ 190.61111111  197.88888889]]
Numpy.cov() function: [[ 328.66666667  228.73333333]
 [ 228.73333333  237.46666667]]

这是为什么呢？ numpy.cov()函数是如何实现的？如果函数 numpy.cov() 实现良好，我做错了什么？我只是说，我的函数 covariance() 的结果与互联网上用于计算协方差系数的 paper 示例的结果一致，例如 http://www.naukowiec.org/wzory/statystyka/kowariancja_11.html .

Answer 1

numpy 函数的默认设置与您的不同。试试看

>>> np.cov([X, Y], ddof=0)
array([[ 273.88888889,  190.61111111],
       [ 190.61111111,  197.88888889]])

引用资料:

• http://docs.scipy.org/doc/numpy/reference/generated/numpy.cov.html
• http://en.wikipedia.org/wiki/Covariance#Calculating_the_sample_covariance