simulate.py

def importance_sampling_MC(lamda, num_samples):
    A = lamda
    
    running_total = 0
    for i in range(num_samples):
        r = get_rand_number(0,1)
        running_total += f_of_x(inverse_G_of_r(r, lamda=lamda))/g_of_x(inverse_G_of_r(r, lamda=lamda), A, lamda)
    approximation = float(running_total/num_samples)
    return approximation

# run simulation
num_samples = 10000
approx = importance_sampling_MC(optimal_lamda, num_samples)
variance = get_IS_variance(optimal_lamda, num_samples)
error = (variance/num_samples)**0.5

# display results
print(f"Importance Sampling Approximation: {approx}")
print(f"Variance: {variance}")
print(f"Error: {error}")