ENH: Von Mises distribution fit - #17585

Test failures come from von_mises_line, not von_mises itself. Had not checked those tests before but was able to reproduce locally now. I am not sure how to best proceed with it.

The only easy but probably tedious solution to me seems to make von_mises_line its own distribution. Currently it is just another instance of von_mises.

Implemented a check if the distribution is an instance of vonmises_line by checking its support. Not pretty but solved the problem AFAICS.

The latest CI failure seems unrelated to this PR.

The latest CI failure seems unrelated to this PR.

FYI, we have some failures in main as well on Linux and Cirrus is flaky.

More extensive testing results for $\mu=\frac{\pi}{2}$ and varying $\kappa$.

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

def test_fit(mu_ref, kappa_ref, n_samples, n_trials):
    angular_errors = np.zeros((n_trials, ))
    kappa_fitted = np.zeros((n_trials, ))

    for i in range(n_trials):
        samples = stats.vonmises(loc=mu_ref, kappa=kappa_ref).rvs(n_samples)
        mu, kappa =stats.vonmises.fit(samples)
        kappa_fitted[i] = kappa 
        angular_errors[i] = np.arccos(np.cos(mu)*np.cos(mu_ref) + np.sin(mu)*np.sin(mu_ref))
    mu_error_avg = np.mean(angular_errors)
    kappa_rel_error_avg = np.mean(np.abs((kappa_fitted - kappa_ref))/kappa_ref)
    return mu_error_avg, kappa_rel_error_avg

mu_ref = 0.5 * np.pi
kappas = np.linspace(0.1, 100, 50)
mu_mean_angular_error = np.zeros_like(kappas)
kappa_mean_rel_error = np.zeros_like(kappas)
for index, kappa in enumerate(kappas):
    mu_error_avg, kappa_rel_error_avg = test_fit(mu_ref=mu_ref, kappa_ref=kappa, n_samples=100000, n_trials=50)
    mu_mean_angular_error [index] = mu_error_avg
    kappa_mean_rel_error[index] = kappa_rel_error_avg

plt.plot(kappas, mu_mean_angular_error , label="$\mu$ angular error")
plt.plot(kappas, kappa_mean_rel_error, label="$\kappa$ relative error")
plt.xlabel("$\kappa$")
plt.legend()

From my side this is ready for review again.

Changes:

• The fit method only accpets data in the range [-pi, pi] now to comply with the support of the distribution.
• The PR only affects vonmises, not vonmises_line

Thanks @tupui :).

Just noticed one thing though: technically, this might break something because so far vonmises.fit accepted any data I think. CC @mdhaber

The fit method only accpets data in the range [-pi, pi] now

Why not wrap the data?

The fit method only accpets data in the range [-pi, pi] now

Why not wrap the data?

I am always a little sceptical when a user can input pretty much anything. But here you are probably right that it is the better solution, people might be relying on this.

So in principle it would be enough to add np.mod(data, 2*np.pi) before and add a test with shifted/non shifted data.

But then maybe we need some notes in the doc if we don't want a warning.

@tupui @mdhaber feel free to push to this branch whatever is needed to get this over the finish line, from my side the math and tests are done.