Calculation of outlier score in series_outlier method

I want to implement the series_outlier method in Python & used the following code

import pandas as pd
import numpy as np
from scipy.stats import norm

# Load the data into a DataFrame
data = {
    'series': [67.95675, 58.63898, 33.59188, 4906.018, 5.372538, 702.1194, 0.037261, 11161.05, 1.403496, 100.116]
     }
  df = pd.DataFrame(data)

  # Function to calculate the outlier score based on custom percentiles
def custom_percentile_outliers(series, p_low=10, p_high=90):
   # Calculate custom percentiles
   percentile_low = np.percentile(series, p_low)
    percentile_high = np.percentile(series, p_high)

    # Calculate Z-scores for the percentiles assuming normal distribution
    z_low = norm.ppf(p_low / 100)
z_high = norm.ppf(p_high / 100)

# Calculate normalization factor
normalization_factor = (2 * z_high - z_low) / (2 * z_high - 2.704)

# Calculate outliers score
return series.apply(lambda x: (x - percentile_high) / (percentile_high - percentile_low) * normalization_factor
                   if x > percentile_high else ((x - percentile_low) / (percentile_high - percentile_low) * normalization_factor
                   if x < percentile_low else 0))

 # Apply the custom percentile outlier scoring function
 df['outliers'] = custom_percentile_outliers(df['series'], p_low=10, p_high=90)

# Display the DataFrame with outliers
 print(df)

And getting the following results for the series

     series   outliers

0 67.956750 0.000000 1 58.638980 0.000000 2 33.591880 0.000000 3 4906.018000 0.000000 4 5.372538 0.000000 5 702.119400 0.000000 6 0.037261 0.006067 7 11161.050000 -27.776847 8 1.403496 0.000000 9 100.116000 0.000000

While with the series_outlier function I get the below results

I referred the github article https://github.com/microsoft/Kusto-Query-Language/issues/136 & also tried implementing & manually calculating with the help of the solution given on stackoverflow - How does Kusto series_outliers() calculate anomaly scores?

I am probably going wrong with the normalization score calculation. Would be great if someone can help

You can use below code to use series_outlier method:

import pandas as r
from scipy.stats import norm as r_nm
import numpy as rn

rith_test = {
    'r_sr': [67.95675, 58.63898, 33.59188, 4906.018, 5.372538, 702.1194, 0.037261, 11161.05, 1.403496, 100.116]
}
rd = r.DataFrame(rith_test)
def test(r_sr, p_l=10, p_h=90):
    rpl = rn.percentile(r_sr, p_l)
    rph = rn.percentile(r_sr, p_h)
    z_low = r_nm.ppf(p_l / 100)
    z_high = r_nm.ppf(p_h / 100)
    rnf = (z_high - z_low) / (rph - rpl)
    def rtst(ri):
        if ri > rph:
            return (ri - rph) * rnf
        elif ri < rpl:
            return (ri - rpl) * rnf
        else:
            return 0
    return r_sr.apply(rtst)
rd['outliers'] = test(rd['r_sr'], p_l=10, p_h=90)
print(rd)