.. _tutorial_norton_bass:

Norton-Bass Model for Generational Substitution
===============================================

This tutorial demonstrates how to use the `NortonBassModel` to simulate the diffusion of successive product generations.

.. code-block:: python

    import numpy as np
    import matplotlib.pyplot as plt
    from innovate.substitute.norton_bass import NortonBassModel

    # Initialize the model for 2 generations
    model = NortonBassModel(n_generations=2)

    # Set the parameters
    model.params_ = {
        "p1": 0.03, "q1": 0.2, "m1": 1000,
        "p2": 0.02, "q2": 0.3, "m2": 1500
    }

    # Generate the time points
    t = np.linspace(0, 50, 100)

    # Predict the diffusion
    y = model.predict(t)

    # Plot the results
    plt.figure(figsize=(10, 6))
    plt.plot(t, y[:, 0], label='Generation 1')
    plt.plot(t, y[:, 1], label='Generation 2')
    plt.title("Norton-Bass Substitution Model")
    plt.xlabel("Time")
    plt.ylabel("Cumulative Adopters")
    plt.grid(True, linestyle='--', alpha=0.6)
    plt.legend()
    plt.show()