Port Generalized von Mises distribution from libDirectional

[Copilot]

Ports GvMDistribution (arbitrary-order Generalized von Mises) from libDirectional, based on Gatto & Jammalamadaka, Statistical Methodology, 2007.

Distribution

• PDF: p(x) = (1/C) · exp(Σⱼ κⱼ · cos(j·(x − μⱼ))) for j = 1…k
• Normalization constant C computed numerically via scipy.integrate.quad and cached
• Order-1 case is mathematically equivalent to standard von Mises

Changes

• pyrecest/distributions/circle/generalized_von_mises_distribution.py — new GvMDistribution subclassing AbstractCircularDistribution
• pyrecest/distributions/__init__.py — exports GvMDistribution
• pyrecest/tests/distributions/test_generalized_von_mises_distribution.py — covers init validation, PDF non-negativity, integrates-to-1, and order-1 equivalence to VonMisesDistribution

from pyrecest.distributions import GvMDistribution
import numpy as np

# Order-1: equivalent to VonMisesDistribution(mu=2.0, kappa=1.0)
gvm1 = GvMDistribution(np.array([2.0]), np.array([1.0]))

# Order-2: second harmonic with separate location/concentration
gvm2 = GvMDistribution(np.array([2.0, 1.0]), np.array([1.0, 0.5]))
xs = np.linspace(0, 2 * np.pi, 100)
gvm2.pdf(xs)  # normalized, integrates to 1

[github-actions]

✅MegaLinter analysis: Success

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	7.05s
✅ JSON	prettier	2	0	0	0	0.46s
✅ JSON	v8r	2		0	0	2.47s
✅ MARKDOWN	markdownlint	1	0	0	0	0.66s
✅ MARKDOWN	markdown-table-formatter	1	0	0	0	0.25s
✅ PYTHON	bandit	252		0	0	3.05s
✅ PYTHON	black	252	0	0	0	4.42s
✅ PYTHON	flake8	252		0	0	1.74s
✅ PYTHON	isort	252	2	0	0	0.48s
✅ PYTHON	mypy	252		0	0	4.07s
✅ PYTHON	pylint	252		0	0	70.96s
✅ PYTHON	ruff	252	2	0	0	0.04s
✅ REPOSITORY	checkov	yes		no	no	22.3s
✅ REPOSITORY	gitleaks	yes		no	no	4.36s
✅ REPOSITORY	git_diff	yes		no	no	0.04s
✅ REPOSITORY	secretlint	yes		no	no	6.13s
✅ REPOSITORY	syft	yes		no	no	3.04s
✅ REPOSITORY	trivy-sbom	yes		no	no	2.29s
✅ REPOSITORY	trufflehog	yes		no	no	18.28s
✅ YAML	prettier	4	0	0	0	0.48s
✅ YAML	v8r	4		0	0	4.9s
✅ YAML	yamllint	4		0	0	0.42s

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[github-actions]

Test Results

    4 files   -     8      4 suites   - 8   19m 58s ⏱️ - 2h 58m 30s
  579 tests +    8    579 ✅ +    8  0 💤 ±    0  0 ❌ ±0 
2 464 runs   - 4 600  2 464 ✅  - 3 416  0 💤  - 1 184  0 ❌ ±0 

Results for commit fcbcb16. ± Comparison against base commit 8d19d73.

♻️ This comment has been updated with latest results.