Compound Distributions

A short tutorial on building compound (mixture) probability distributions in Python and drawing random samples from them.

Reza Ehsani & Hoshin V. Gupta

A compound PDF is a weighted mixture of standard densities:

P(x) = Σ wᵢ · pᵢ(x),   with   Σ wᵢ = 1,   0 < wᵢ < 1

where each pᵢ(x) is a standard PDF (Uniform, Normal, Exponential, ...). The notebook defines a compound_distribution class on top of SciPy's rv_continuous, so the mixture behaves like any other SciPy distribution — its PDF, CDF, and random sampling all come for free — and walks through two worked examples with plots.

Contents

Compound_Distribution.ipynb — the tutorial notebook:

• a compound_distribution(rv_continuous) class that combines any list of SciPy densities under a set of weights
• a plot_compound helper that overlays the PDF, CDF, and a sampled histogram
• Example 1 — Uniform + Normal, 10,000 samples
• Example 2 — Uniform + Normal + Exponential, 50,000 samples

Run it

Open in Colab (badge above), or run locally:

pip install numpy scipy matplotlib
jupyter notebook Compound_Distribution.ipynb

Dependencies

NumPy, SciPy, and Matplotlib.