violin plot with categorization using two different columns of data for "one violin"

trying to visualize the distributions of the data stored in a dataframe.
I have 1000 rows, each of them has next columns:

sample_id | chi_2_n_est | chi_2_n_theo 
---------------------------------------
1         | 1.01        | 1.001 
1         | 1.03        |1.012 
... 
2         | 1.11        | 1.04
3         | 1.21        | 1.03
...

I want to display violin plots for the data stored in columns chi_2_n_est and chi_2_n_theo, but splitter - to compare the distributions for each sample_id in the dataframe.

Something similar to:

Where blue will be the distribution for chi_2_n_est, and orange for chi_2_n_theo for each sample_id...

I don't have your data, but I created a random sample that will hopefully mimic yours. I also misspoke, this is the opposite of a pivot, your data is pivoted

import pandas as pd
import numpy as np
import seaborn as sns

# create dummy data
data = {
    'product_id': np.random.choice(2, 22, replace=True)+1,
    'chi_2_ne': np.random.uniform(0.1, 1.9, 22),
    'chi_2_theo': np.random.uniform(0.1, 1.9, 22)
}

# load into a dataframe
df = pd.DataFrame.from_dict(data)

# use melt to blend columns into rows (opposite of pivot, actually)
pdf = df.melt(id_vars=['product_id'], value_vars=['chi_2_ne', 'chi_2_theo'], var_name='measure', value_name='value')

# use seaborn to create a violin plot where split=True
sns.violinplot(data=pdf, x="product_id", y="value", hue="measure", split=True)

To create

Hopefully this is what you are looking for, and similar enough to your raw data that it's useful. Notes on pd.melt and sns.violinplot if you need it