I’m trying to (1) simulate data with a Weibull distribution using known parameters, and then (2) trying to fit that simulated data with a Weibull function and get parameters back. The idea is that I will ultimately try to fit a Weibull to real data, but I’ve run into problems during very basic testing.

Here’s my code:

from scipy.stats import weibull_min
from scipy.optimize import curve_fit

def weibull(x, shape, loc, scale):
    return weibull_min.pdf(x, shape, loc, scale)

# Create a 3-second timecourse
t_start = 0
t_end = 3
samples = t_end * 100  # simulate 100 samples per second

t = np.linspace(t_start, t_end, samples)

# Set known (kn) parameters for the Weibull distribution
kn_shape, kn_loc, kn_scale = 1.5, 0, 1 

# Generate the Weibull distribution with the known parameters
sim_data = weibull(t, kn_shape, kn_loc, kn_scale)

# Fit the simulated data with a Weibull function and return parameters
params, _ = curve_fit(weibull, t, sim_data_noisy)

The problem is that params should be exactly the same as known_params, but they are not. The following:

print(f'shape = {params[0]}, loc = {params[1]}, scale = {params[2]}')

…returns

shape = 1.4999999989589334, loc = 4.399587587206362e-10, scale =
0.9999999997072269

Of course, all three parameters are pretty damn close to the initial inputs, but I don’t see why they are not identical. Can someone help me understand what is going on here?

I’m running Python 3.10.4 on a Linux server