BUG: Wrong result of Kurtosis

[xitongsys]

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Reproducible Example

a = pd.Series([0,0,0,0,0.00005])

a.kurtosis()
Out[205]: np.float64(0.0)

scipy.stats.kurtosis(a,bias=False)
Out[206]: np.float64(4.999999999999997)

Issue Description

Pandas can't give a right result of kurtosis. But the scipy.stats.kurtosis can.

Expected Behavior

see the code

Installed Versions

Replace this line with the output of pd.show_versions()

[Liam3851]

This appears to be a duplicate of #57972. Seems this is a floating point underflow as the result of a fix to #18044. E.g. in pd.core.nanops.nankurt:

https://github.com/pandas-dev/pandas/blob/7945e563d36bcf4694ccc44698829a6221905839/pandas/core/nanops.py#L1354C2-L1359C47

    # floating point error
    #
    # #18044 in _libs/windows.pyx calc_kurt follow this behavior
    # to fix the fperr to treat denom <1e-14 as zero
    numerator = _zero_out_fperr(numerator)
    denominator = _zero_out_fperr(denominator)

Here the denominator is coming out as 2.4e-17 which is getting set to 0, because the numbers involved are so small.

Not sure how scipy is handling this to make it numerically stable for extremely small values.

[mroeschke]

Closing as a duplicate of #57972