python - 为什么 np.var(x) 和 np.cov(x, y) 给我不同的值？

Question

我是 Python 新手，想知道为什么 np.var(x) 给出的答案与 np.cov(x, y) 输出中找到的 cov(x,x) 值不同。它们不应该是一样的吗？我知道这与偏差或 ddof 有关，与标准化有关，但我不太确定这意味着什么，也找不到任何专门回答我的问题的资源。希望有人能帮忙!

Answer 1

在 numpy 中，cov 默认为“delta 自由度”1，而 var 默认为 ddof 0。从注释到 numpy.var

Notes
-----
The variance is the average of the squared deviations from the mean,
i.e.,  ``var = mean(abs(x - x.mean())**2)``.

The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
If, however, `ddof` is specified, the divisor ``N - ddof`` is used
instead.  In standard statistical practice, ``ddof=1`` provides an
unbiased estimator of the variance of a hypothetical infinite population.
``ddof=0`` provides a maximum likelihood estimate of the variance for
normally distributed variables.

因此，您可以通过以下方式让他们同意:

In [69]: cov(x,x)#defaulting to ddof=1
Out[69]: 
array([[ 0.5,  0.5],
       [ 0.5,  0.5]])

In [70]: x.var(ddof=1)
Out[70]: 0.5

In [71]: cov(x,x,ddof=0)
Out[71]: 
array([[ 0.25,  0.25],
       [ 0.25,  0.25]])

In [72]: x.var()#defaulting to ddof=0
Out[72]: 0.25