How to find skewness and kurtosis correctly in pandas?

bias=False

print(
    stats.kurtosis(x, bias=False), pd.DataFrame(x).kurtosis()[0],
    stats.skew(x, bias=False), pd.DataFrame(x).skew()[0],
    sep='\n'
)

-0.31467107631025515
-0.31467107631025604
-0.4447887763159889
-0.444788776315989

Pandas calculate UNBIASED estimator of the population kurtosis. Look at the Wikipedia for formulas: https://www.wikiwand.com/en/Kurtosis

Calculate kurtosis from scratch

import numpy as np
import pandas as pd
import scipy

x = np.array([0, 3, 4, 1, 2, 3, 0, 2, 1, 3, 2, 0,
              2, 2, 3, 2, 5, 2, 3, 999])
k2 = x.var(ddof=1) # default numpy is biased, ddof = 0
sum_term = ((x-xbar)**4).sum()
factor = (n+1) * n / (n-1) / (n-2) / (n-3)
second = - 3 * (n-1) * (n-1) / (n-2) / (n-3)

first = factor * sum_term / k2 / k2

G2 = first + second
G2 # 19.998428728659768

Calculate kurtosis using numpy/scipy

scipy.stats.kurtosis(x,bias=False) # 19.998428728659757

Calculate kurtosis using pandas

pd.DataFrame(x).kurtosis() # 19.998429

Similarly, you can also calculate skewness.