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A property of the covariance is, that cov(x, x) = var(x)
However, in numpy I don't get the same result.
from numpy import var, cov
x = range(10)
y = var(x)
z = cov(x, x)[0][1]
print y, z
Am I doing something wrong here? How can I obtain the correct result?
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cov() function. Covariance provides the a measure of strength of correlation between two variable or more set of variables. The covariance matrix element Cij is the covariance of xi and xj. The element Cii is the variance of xi.
The variance is the average of the squared deviations from the mean, i.e., var = mean(x) , where x = abs(a - a. mean())**2 . The mean is typically calculated as x. sum() / N , where N = len(x) .
The covariance may be computed using the Numpy function np. cov() . For example, we have two sets of data x and y , np. cov(x, y) returns a 2D array where entries [0,1] and [1,0] are the covariances. Entry [0,0] is the variance of the data in x , and entry [1,1] is the variance of the data in y .
You must use z=cov(x,bias=1) in order to normalize by N ,because var is also norm by N (according to this
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