Norton-Bass Model for Generational Substitution

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

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()