Don't understand why these two Python functions give different results

Question

I have these two functions here giving different results, but I do not understand why, and assuming the second one is the correct one for Parkinson volatility, how to modify the first one to obtain the same results for the second one. This is the original formula: Parkinson volatility

This is the code:

def Parkinson1(price, window):
  sigmasqrd = (1.0 / (4.0 * math.log(2.0))) * ((price['High'] / price['Low']).apply(np.log))**2.0
  sigmasqrd_mean=sigmasqrd.rolling(window).mean()
  sigma=(252*sigmasqrd)**0.5
  sigma=sigma.rolling(window).mean()
  return sigma

def Parkinson2(price, window, trading_periods=252, clean=True):

    rs = (1.0 / (4.0 * math.log(2.0))) * ((price['High'] / price['Low']).apply(np.log))**2.0

    def f(v):
        return (trading_periods * v.mean())**0.5
    
    result = rs.rolling(
        window=window,
        center=False
    ).apply(func=f)
    
    if clean:
        return result.dropna()
    else:
        return result

df['Parkinson1']=Parkinson1(df, window=22)
df['Parkinson2']=Parkinson2(df, window=22)
df.tail(10)

            Date        Open        High       Low         Close    Adj Close     Volume       vwap      Pct         Returns    Parkinson1   Parkinson2
1249    2020-03-16  241.179993  256.899994  237.360001  239.850006  233.172028  297240000   241.179993  -0.109424   1.151741    0.347854    0.413066
1250    2020-03-17  245.039993  256.170013  237.070007  252.800003  245.761459  262070500   245.039993  0.053992    1.213926    0.378139    0.441803
1251    2020-03-18  236.250000  248.369995  228.020004  240.000000  233.317871  327597100   236.250000  -0.050633   1.152461    0.413217    0.474653
1252    2020-03-19  239.250000  247.380005  232.220001  240.509995  233.813660  289322000   239.250000  0.002125    1.154910    0.437453    0.491526
1253    2020-03-20  242.529999  244.470001  228.500000  228.800003  223.737640  347158800   242.529999  -0.048688   1.098679    0.464679    0.510255
1254    2020-03-23  228.190002  229.679993  218.259995  222.949997  218.017059  326025200   228.190002  -0.025568   1.070588    0.480385    0.519814
1255    2020-03-24  234.419998  244.100006  233.800003  243.149994  237.770142  235494500   234.419998  0.090603    1.167587    0.494879    0.526782
1256    2020-03-25  244.869995  256.350006  239.750000  246.789993  241.329590  299430300   244.869995  0.014970    1.185066    0.507582    0.538669
1257    2020-03-26  249.520004  262.799988  249.050003  261.200012  255.420761  257632800   249.520004  0.058390    1.254262    0.513269    0.543397
1258    2020-03-27  253.270004  260.809998  251.050003  253.419998  247.812912  224341200   253.270004  -0.029786   1.216903    0.519583    0.546804

Answer 1

It seems that you are using price in Parkinson1 .

While you're using price_data in Parkinson2 .