Hey there! Great question—even if you worried it might not fit the forum, this is exactly the kind of detail that helps folks get comfortable with how SciPy's statistical tools work under the hood. Let's dive in:

You’re spot-on: this method uses Maximum Likelihood Estimation (MLE) to estimate the normal distribution’s mean (loc parameter) and standard deviation (scale parameter) from your dataset.

Here’s the breakdown for normal distributions: #

For a normal distribution (N(\mu, \sigma^2)), MLE gives us closed-form solutions (no fancy iterative math needed here):

• The estimated mean (\hat{\mu}) is simply the sample mean of your data
• The estimated standard deviation (\hat{\sigma}) is the square root of the average squared deviation from the sample mean (note: this uses the full sample size (n) in the denominator, not (n-1) like the unbiased sample standard deviation)

Why you might not see this spelled out in official docs #

SciPy’s docs don’t always explicitly call out MLE for every distribution’s fit() method, but you can confirm this easily:

• Check the source code: norm.fit() inherits from the generic rv_continuous.fit() method. For the normal distribution, the implementation directly computes the MLE estimates using the sample mean and the MLE variance (since there’s a closed-form solution).
• Test with sample data: Generate a dataset with known normal parameters, run norm.fit(), and you’ll get estimates almost identical to your true values (accounting for small sampling error). Here’s a quick example:

import numpy as np
from scipy.stats import norm

# Generate data with known mean=5, std=2
np.random.seed(42)
sample_data = norm.rvs(loc=5, scale=2, size=1000)

# Fit the distribution
estimated_mean, estimated_std = norm.fit(sample_data)

print(f"Estimated mean: {estimated_mean:.2f}")  # Outputs ~5.0
print(f"Estimated std: {estimated_std:.2f}")    # Outputs ~2.0

For other distributions where MLE doesn’t have a simple closed-form solution, fit() uses iterative optimizers like BFGS to find the parameters that maximize the likelihood, but the normal distribution is nice and straightforward.

内容的提问来源于stack exchange，提问作者BillyJo_rambler