How Can Scipy Help Determine the Best-Fitting Theoretical Distribution for Empirical Data?

Fitting Empirical Distributions to Theoretical Ones with Scipy (Python)

Introduction:

Given a list of observed values from an unknown distribution, it is often desirable to fit them to a theoretical distribution to estimate probabilities and determine the best-fitting model. This article explores how to implement such an analysis in Python using Scipy and provides a detailed example of fitting various distributions to the El Niño dataset.

Method:

To determine the best-fitting distribution, we can use the sum of square errors (SSE) between the histogram of the observed data and the probability density function (PDF) of the fitted distribution. The distribution with the lowest SSE is considered the best fit.

Implementation:

1. Import necessary modules (Scipy, NumPy, Matplotlib).
2. Define a function to fit distributions to data and calculate SSE.

3. For each distribution in the Scipy distribution list:

   • Fit the distribution to the data.
   • Calculate the SSE.
4. Return the distribution with the lowest SSE.

Additional Features:

• Plot the fitted distributions for visualization.
• Generate the PDF of the best-fitting distribution.

Example:

Using the El Niño dataset, we fit multiple distributions to the data and determine the best fit based on SSE. The results show that the "genextreme" distribution provides the best fit.

Code:

The provided code includes the steps mentioned above and displays the fitted distributions and PDF in interactive plots.

Conclusion:

By utilizing the Scipy library in Python, we can easily fit empirical distributions to theoretical ones and determine the best-fitting model based on SSE. This technique allows for a data-driven approach to modeling and probability estimation.

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