BUG: Inconsistent returns of Series.kurt() and Series.rolling().kurt() and scipy.stats.kurtosis(s, bias=False)

[ysq151944]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import numpy as np
import pandas as pd
import scipy


s = pd.Series(
    [1.02578894e-05, 1.02293423e-05, 1.01612350e-05, 1.01349948e-05,
       1.01160014e-05, 1.01576422e-05, 1.00931034e-05, 1.03640110e-05,
       1.02877454e-05, 1.01952724e-05, 1.01890684e-05, 1.00791466e-05,
       1.01313970e-05, 1.01277183e-05, 1.00960879e-05, 1.01652324e-05,
       1.02296093e-05, 1.00787941e-05, 1.01104972e-05, 1.01003808e-05,
       1.00734780e-05, 1.01441318e-05, 1.01006246e-05, 1.01138324e-05,
       1.02339181e-05, 1.00859402e-05, 1.03746594e-05, 1.01465576e-05,
       1.02368692e-05, 1.02153110e-05, 1.01311249e-05, 1.01408451e-05,
       1.01011158e-05, 1.00280505e-05, 1.00897790e-05, 1.00418994e-05,
       1.01514109e-05, 1.00626523e-05, 1.00911641e-05, 1.00627834e-05,
       1.01141079e-05, 1.00997592e-05, 1.01507366e-05, 1.02640487e-05,
       1.00593161e-05, 1.00563380e-05, 1.02594258e-05, 1.00971885e-05,
       1.01073036e-05, 1.01400070e-05, 1.01543860e-05, 1.00726644e-05,
       1.01515152e-05, 1.01142659e-05, 1.01246537e-05, 1.01032702e-05,
       1.00522466e-05, 1.00515818e-05, 1.00793651e-05, 1.00864454e-05,
       1.00735809e-05, 1.00688942e-05, 1.00827586e-05, 1.01284276e-05,
       1.00683060e-05, 1.00381018e-05, 1.00869565e-05, 1.00312935e-05,
       1.02813559e-05, 1.01728228e-05, 1.02937158e-05, 1.03638218e-05,
       1.00987066e-05, 1.01727642e-05, 1.00686342e-05, 1.01320957e-05,
       1.01650861e-05, 1.01500349e-05, 1.00657212e-05, 1.00931999e-05,
       1.00447967e-05, 1.01139896e-05, 1.01117318e-05, 1.01278066e-05,
       1.01005548e-05, 1.01563031e-05, 1.00586005e-05, 1.00658123e-05,
       1.01146231e-05, 1.00964519e-05, 1.00308642e-05, 1.00490540e-05,
       1.00175316e-05, 1.00632911e-05, 1.01267992e-05, 1.00593575e-05,
       1.00489853e-05, 1.00248668e-05, 1.00351000e-05, 1.00742574e-05,
       1.02523014e-05, 1.00687521e-05, 1.00593575e-05, 1.00939457e-05,
       1.01066391e-05, 1.03319502e-05, 1.01693158e-05, 1.00928793e-05,
       1.00388555e-05, 1.00883704e-05, 1.00249377e-05, 1.00321199e-05,
       1.01396161e-05, 1.00418118e-05, 1.00614964e-05, 1.00318359e-05,
       1.00837404e-05, 1.01211073e-05, 1.01129750e-05, 1.02277362e-05,
       1.00823328e-05, 1.01399795e-05, 1.00868659e-05, 1.00453911e-05,
       1.02066116e-05, 1.00927516e-05, 1.00688705e-05, 1.01990391e-05,
       1.00892244e-05, 1.00277681e-05, 1.00926561e-05, 1.01122449e-05,
       1.01172818e-05, 1.01734694e-05, 1.01435897e-05, 1.00908773e-05,
       1.00523013e-05, 1.00488315e-05, 1.00630032e-05, 1.00618769e-05,
       1.00208406e-05, 1.00556328e-05, 1.01460102e-05, 1.01463083e-05,
       1.01481226e-05, 1.00790650e-05, 1.02364633e-05, 1.01442308e-05,
       1.02065404e-05, 1.01475129e-05, 1.00382476e-05, 1.00350631e-05,
       1.01062008e-05, 1.02846365e-05, 1.02376852e-05, 1.01319444e-05,
       1.02561475e-05, 1.03181049e-05, 1.01535836e-05, 1.01095515e-05,
       1.01876493e-05, 1.01786328e-05, 1.02526954e-05, 1.02585034e-05,
       1.01950051e-05, 1.01134410e-05, 1.01499659e-05, 1.01989708e-05,
       1.01404110e-05, 1.05155343e-05, 1.09902978e-05, 1.01428086e-05,
       1.03182290e-05, 1.02584155e-05, 1.04534687e-05, 1.01995940e-05,
       1.02676152e-05, 1.01541624e-05, 1.01789936e-05, 1.01260218e-05,
       1.01322034e-05, 1.00410818e-05, 1.00686813e-05, 1.01616231e-05,
       1.00586005e-05, 1.00760719e-05, 1.00624350e-05, 1.01486346e-05,
       1.02006803e-05, 1.01121626e-05, 1.01031637e-05, 1.03890392e-05,
       1.00863558e-05, 1.00523195e-05, 1.00707714e-05, 1.00823893e-05,
       1.01415257e-05, 1.00789835e-05, 1.00495575e-05, 1.00885897e-05,
       1.00692281e-05, 1.00771388e-05, 1.00620048e-05, 1.00284091e-05,
       1.01131142e-05, 1.00388281e-05, 1.00284293e-05, 1.00951710e-05,
       1.01274544e-05, 1.03340220e-05, 1.00520472e-05, 1.00418118e-05,
       1.00593368e-05, 1.02079782e-05, 1.02583534e-05, 1.00416378e-05,
       1.00726644e-05, 1.01064585e-05, 1.01246537e-05, 1.01015051e-05,
       1.00830737e-05, 1.00430416e-05, 1.00683453e-05, 1.00498575e-05,
       1.00566773e-05, 1.00666901e-05, 1.01006246e-05, 1.01069334e-05,
       1.05375978e-05, 1.00688231e-05, 1.00418118e-05, 1.00388693e-05,
       1.00313152e-05, 1.00385019e-05, 1.00808152e-05, 1.02655807e-05,
       1.00556715e-05, 1.00742837e-05, 1.01517889e-05, 1.00073126e-05,
       1.00218341e-05, 1.00383008e-05, 1.00176741e-05, 1.00943396e-05,
       1.01277624e-05, 1.00668308e-05, 1.01045661e-05, 1.01406470e-05,
       1.01005199e-05, 1.00320513e-05, 1.00427350e-05, 1.00634473e-05,
       1.00250000e-05, 1.00608665e-05, 1.00595447e-05, 1.00212691e-05,
       1.00901838e-05, 1.01518288e-05, 1.00770308e-05, 1.00646320e-05,
       1.00214746e-05, 1.02915952e-05, 1.01373626e-05, 1.00936200e-05,
       1.00607577e-05, 1.01227639e-05, 1.00495225e-05, 1.00758123e-05,
       1.02173139e-05, 1.01211073e-05, 1.00486618e-05, 1.00870777e-05,
       1.01042753e-05, 1.00671853e-05, 1.01027046e-05, 1.00350018e-05,
       1.00866251e-05, 1.01004503e-05, 1.01476793e-05, 1.00390625e-05,
       1.01483270e-05, 1.00491918e-05, 1.00955076e-05, 1.01203990e-05,
       1.01119272e-05, 1.01684211e-05, 1.00920680e-05, 1.00313917e-05])

print(
    s.kurt(),
    s.rolling(s.size).kurt().iloc[-1],
    scipy.stats.kurtosis(s, bias=False)
)  # 0 nan 22.23117509831192

Issue Description

The returns should be the same, yet:

1. s.kurt() -- 0
2. s.rolling(s.size).kurt().iloc[-1] -- nan
3. scipy.stats.kurtosis(s, bias=False) -- 22.23117509831192

Expected Behavior

should return the value of scipy.stats.kurtosis(s, bias=False), which is 22.231170213891627 in this case.

Installed Versions

INSTALLED VERSIONS

commit : 965ceca
python : 3.11.3.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.0-57-generic
Version : #63-Ubuntu SMP Thu Nov 24 13:43:17 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : zh_CN.UTF-8
LOCALE : zh_CN.UTF-8

pandas : 2.0.2
numpy : 1.24.3
pytz : 2023.3
dateutil : 2.8.2
setuptools : 67.8.0
pip : 23.0.1
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : 8.13.2
pandas_datareader: None
bs4 : None
bottleneck : None
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 12.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.10.1