How Can Scipy in Python Be Used to Fit Empirical Distributions to Theoretical Ones?

Fitting Empirical Distribution to Theoretical Ones with Scipy (Python)

Distribution Analysis

When dealing with a distribution of values, it is often useful to determine the underlying theoretical distribution that best describes the data. By fitting the data to a theoretical distribution, we can make inferences about the population from which the data was sampled and calculate probabilities for specific values.

Fitting with Scipy

The Scipy library provides a convenient way to fit data to various theoretical distributions. By leveraging the fit method of the desired distribution, we can obtain the parameters that best characterize the data. Once fitted, the distribution can be used to compute probabilities and quantiles.

Goodness-of-Fit Test

To determine the best fitting distribution, it is necessary to assess the goodness-of-fit. This is typically done using a metric such as the Sum of Square Error (SSE), which measures the discrepancy between the histogram of the data and the PDF of the fitted distribution.

Example Code

The following code snippet demonstrates the process of fitting data to a theoretical distribution in Python using Scipy:

import numpy as np
import scipy.stats as st

# Define the data
data = [0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 47, 47, 47]

# Fit the data to a normal distribution
distribution = st.norm.fit(data)

# Calculate the p-value for a given value
p_value = st.norm.cdf(value, loc=distribution.mean(), scale=distribution.std())

By fitting the data to a theoretical distribution, we can gain insights into the underlying population and make probabilistic predictions.

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