How can I sample a Pandas DataFrame with a normal distribution bias?

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I'm trying to sample rows from a Pandas DataFrame such that the selection is biased according to a normal (Gaussian) distribution. I initially attempted to use the random_state parameter of the sample method combined with numpy.random.Generator.normal() to achieve this by seeding the sample based on a normally distributed value. However, this approach doesn't work because random_state is only meant for reproducibility with uniform random sampling.

For example:

PYTHON
import pandas as pd
import numpy as np
import random

# Generate a list of unique random numbers
temp = random.sample(range(1, 101), 100)
df = pd.DataFrame({'temperature': temp})

# Sample normal
rng = np.random.default_rng()
triangle_df.sample(n=10, random_state=rng.normal())

This clearly fails because random_state cannot be used to change the underlying sampling distribution. If the goal is to bias your sampling (for instance, to favor rows near the mean), you need to compute weights (e.g., using a normal probability density function) and pass them to the weights parameter in the sample method. The random_state parameter should only be used for ensuring reproducibility.

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Answers 2

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2 Answers

Answer by StackOverflow TychoAI Agent • 1 month ago

Below is an explanation and a working workaround.

Explanation

The random_state parameter in the sample method is used to seed the underlying pseudo‐random number generator. This ensures reproducible results when drawing uniformly at random.
Calling something like rng.normal() returns a single float drawn from a normal (Gaussian) distribution. This is not a valid seed (or generator) but just a numeric sample.
In other words, you cannot change the sampling distribution (from uniform to normal) by using the random_state parameter. The sampling method always picks rows uniformly at random.

Workaround: Weighted Sampling

If you want the sampling to be biased so that some rows have a higher chance of being selected (for example, following a normal distribution), you can compute weights for each row and pass them to the weights parameter.

For example, suppose you want rows whose values are closer to (or further from) the mean to have higher probability as given by a normal pdf. You can do something like this:

PYTHON
import pandas as pd
import numpy as np
import random
from scipy.stats import norm  # used to compute the normal probability density function

# Generate a list of unique random numbers
temp = random.sample(range(1, 101), 100)
df = pd.DataFrame({'temperature': temp})

# Suppose you want to bias the sampling according to a normal distribution
# Compute weights based on a normal pdf. For example:
mu, sigma = df['temperature'].mean(), 15  # you can adjust sigma as needed
weights = norm.pdf(df['temperature'], loc=mu, scale=sigma)
weights /= weights.sum()  # normalize so weights sum to 1

# Now sample 10 rows using these weights and a fixed random state for reproducibility.
df_sampled = df.sample(n=10, weights=weights, random_state=42)
print(df_sampled)

Summary

You cannot substitute the standard uniform sampling of DataFrame.sample by directly passing a sample from a normal distribution via random_state.
Instead use the weights parameter to achieve non-uniform, biased sampling, while keeping random_state solely for reproducibility.

This approach allows you to effectively “simulate” sampling with a given probability distribution (normal in this example) without misusing the random_state parameter.

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Answer by StellarKeeper265 • 1 month ago

Passing a Generator to sample just changes the way the generator is initialized, it won't change the distribution that is used. Random sampling is uniform (choice is used internally [source]) and you can't change that directly with the random_state parameter.

Also note that normal sampling doesn't really make sense for discrete values (like the rows of a DataFrame).

Now let's assume that you want to sample the rows of your DataFrame in a non-uniform way (for example with weights that follow a normal distribution) you could use the weights parameter to pass custom weights for each row.

Here is an example with normal weights (although I'm not sure if this makes much sense):

PYTHON
rng = np.random.default_rng()
weights = abs(rng.normal(size=len(df)))

sampled = df.sample(n=10000, replace=True, weights=weights)

Another example based on this Q/A. Here we'll give higher probabilities to the rows from the middle of the DataFrame:

PYTHON
from scipy.stats import norm

N = len(df)
weights = norm.pdf(np.arange(N)-N//2, scale=5)
df.sample(n=10, weights=weights).sort_index()

Output (mostly rows around 50):

    temperature
43           94
44           50
47           80
48           99
50           63
51           52
52            1
53           20
54           41
63            3

How can I sample a Pandas DataFrame with a normal distribution bias?

2 Answers

Explanation

Workaround: Weighted Sampling

Summary

Discussion

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