how is pandas kurtosis defined?

Question

I am trying to get kurtosis using pandas. By doing some exploration, I have

test_series = pd.Series(np.random.randn(5000))
test_series.kurtosis()

however, the output is:

-0.006755982906479385

But I think the kurtosis (https://en.wikipedia.org/wiki/Kurtosis) should be close to (maybe normalize over N-1 instead of N, but this does not matter here)

(test_series - test_series.mean()).pow(4).mean()/np.power(test_series.std(),4)

which is

2.9908543104146026

Answer 1

The pandas documentation says the following

Return unbiased kurtosis over requested axis using Fisher’s definition of kurtosis (kurtosis of normal == 0.0)

This is probably the excess kurtosis, defined as kurtosis - 3.