基于等式,我有自己的协方差函数实现:
'''
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()
获得了不同的值,即:
My function: [[ 273.88888889 190.61111111]
[ 190.61111111 197.88888889]]
Numpy.cov() function: [[ 328.66666667 228.73333333]
[ 228.73333333 237.46666667]]
为什么?如何实现numpy.cov()
功能?如果函数numpy.cov()
得到很好的实现,我做错了什么?我只想说,我的函数covariance()
的结果与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。
答案 0 :(得分:16)
numpy函数与您的规范化具有不同的默认设置。尝试改为
>>> np.cov([X, Y], ddof=0)
array([[ 273.88888889, 190.61111111],
[ 190.61111111, 197.88888889]])
参考文献: