Understanding Percentiles and Quantile Calculation

Percentiles are values that separate data into equal-sized groups when data is sorted in ascending or descending order. The most commonly used percentiles are the 25th percentile (also known as the first quartile, Q1), the 50th percentile (Q2 or median), the 75th percentile (third quartile, Q3), and the 95th percentile (also known as the upper percentage point, P95). In this article, we will explore how to calculate percentiles for unique identifiers using Pandas.

Introduction to Pandas

Pandas is a powerful Python library used for data manipulation and analysis. It provides data structures like Series (1-dimensional labeled array) and DataFrames (2-dimensional labeled data structure with columns of potentially different types). DataFrames are ideal for storing and manipulating tabular data, which makes them perfect for problems involving percentiles.

Calculating Percentiles using Pandas

One way to calculate percentiles is by directly applying the quantile function in pandas. However, this approach doesn’t provide the exact percentile value because it uses interpolation between two known data points (the nearest lower and upper quartile values). If you need an exact percentile calculation without any interpolation, we have to manually compute the quantile.

Manual Quantile Calculation using Pandas

We can create a custom function called quantile_exc to calculate the exact percentiles for each unique identifier. The function sorts the data by column, computes the rank of the desired percentile, and then returns the value at that rank.

# Define the quantile_exc function to compute exact percentiles
def quantile_exc(ser, q):
    ser_sorted = ser.sort_values()
    rank = q * (len(ser) + 1) - 1
    assert rank > 0, 'quantile is too small'
    rank_l = int(rank)
    return ser_sorted.iat[rank_l] + (ser_sorted.iat[rank_l + 1] -
                                     ser_sorted.iat[rank_l]) * (rank - rank_l)

Applying the quantile_exc function to DataFrames

To apply this custom quantile calculation function to a DataFrame, we can iterate through each unique identifier and call our helper function.

# Function to calculate percentiles for each unique ID
def test(percentile_staging):
    df = pd.DataFrame(percentile_staging)
    head = df.head()
    print(head)
    
    # Apply quantile_exc on the 'hardened_print_length' series for each unique ID
    percentiles = {}
    for id in df['pm_lookup'].unique():
        id_df = df[df['pm_lookup'] == id]
        fifty = quantile_exc(id_df['hardened_print_length'], 0.5)
        seventy_five = quantile_exc(id_df['hardened_print_length'], 0.75)
        ninety_five = quantile_exc(id_df['hardened_print_length'], 0.95)
        
        percentiles[id] = {'50th Percentile': fifty, 
                           '75th Percentile': seventy_five, 
                           '95th Percentile': ninety_five}
    return pd.DataFrame(percentiles)

Using the pandas.Grouper function

However, we can further optimize our code to improve performance by using pandas.Grouper. Here is how you can do it:

# Function to calculate percentiles for each unique ID
def test(percentile_staging):
    df = pd.DataFrame(percentile_staging)
    head = df.head()
    print(head)

    # Group the DataFrame by 'pm_lookup' and apply quantile_exc on 'hardened_print_length'
    grouped_df = df.groupby('pm_lookup')['hardened_print_length'].apply(quantile_exc, args=(0.5,))
    
    return pd.DataFrame({
        'pm_lookup': grouped_df.index,
        '50th Percentile': grouped_df[0],
        '75th Percentile': grouped_df[1],
        '95th Percentile': grouped_df[2]
    })

Additional Tips and Best Practices

• When using quantile_exc, you should be aware that the input data is expected to be in ascending order. If your data is not sorted, you will need to sort it first.
• Be cautious when applying this function to a DataFrame with missing values, as Pandas does not support percentiles for missing values.

Conclusion

Calculating percentiles by unique identifiers using Pandas can be accomplished with a custom function or the pandas.Grouper method. Both methods offer different solutions depending on your specific needs and performance requirements.

Last modified on 2025-01-29