feat(distributions): add lognakagami, loggamma, and kl_statistic
Implement two new scipy-compatible distributions : Log-Nakagami (lognakagami) and Log-Gamma (loggamma_dist), with complete logpdf/cdf/ppf/stats/entropy/rvs methods derived from the change-of-variable Y = ln(X). Add kl_statistic, a KDE-based KL-divergence goodness-of-fit callable compatible with the Fitter class. Extend k_gen with _stats (improving speed), _cdf, and a fit guard, and switch kv → kve to improve numerical stability at large arguments. Add unit tests for all three additions covering normalization, monotonicity, ppf inversion, moment formulas, and Fitter integration.
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@@ -1,12 +1,13 @@
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import numpy as np
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import pytest
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import scipy.special as sc
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import matplotlib.pyplot as plt
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import sys
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import os
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sys.path.insert(0, os.path.join(os.path.dirname(__file__), ".."))
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from tools.distributions import k_dist
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from tools.distributions import k_dist, lognakagami, loggamma_dist
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X = np.linspace(0.01, 10.0, 500)
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@@ -167,6 +168,178 @@ class TestKDistPlots:
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# ── Entry-point: run plots interactively ─────────────────────────────────────
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Y = np.linspace(-5.0, 5.0, 500)
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# ── lognakagami unit tests ────────────────────────────────────────────────────
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class TestLogNakagami:
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def test_logpdf_is_finite_on_real_line(self):
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"""logpdf must be finite for all real y — tests positivity without float64 underflow."""
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log_vals = lognakagami.logpdf(Y, m=2.0, Omega=1.0)
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assert np.all(np.isfinite(log_vals))
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def test_pdf_integrates_to_one(self):
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"""Numerical integral of PDF over the real line should be ≈ 1."""
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y_fine = np.linspace(-30, 10, 200_000)
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integral = np.trapezoid(lognakagami.pdf(y_fine, m=2.0, Omega=1.0), y_fine)
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assert pytest.approx(integral, abs=1e-3) == 1.0
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def test_pdf_integrates_to_one_nonunit_omega(self):
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"""Normalisation must hold for Omega != 1."""
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y_fine = np.linspace(-30, 15, 200_000)
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integral = np.trapezoid(lognakagami.pdf(y_fine, m=2.0, Omega=4.0), y_fine)
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assert pytest.approx(integral, abs=1e-3) == 1.0
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def test_logpdf_equals_log_pdf(self):
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"""logpdf must equal log(pdf) at points where pdf does not underflow."""
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y_bulk = np.linspace(-4.0, 2.0, 50)
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log_via_pdf = np.log(lognakagami.pdf(y_bulk, m=2.0, Omega=1.0))
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log_direct = lognakagami.logpdf(y_bulk, m=2.0, Omega=1.0)
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np.testing.assert_allclose(log_direct, log_via_pdf, rtol=1e-6)
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def test_cdf_is_monotone_increasing(self):
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"""CDF must be strictly non-decreasing."""
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cdf_vals = lognakagami.cdf(Y, m=2.0, Omega=1.0)
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assert np.all(np.diff(cdf_vals) >= 0)
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def test_ppf_inverts_cdf(self):
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"""ppf(cdf(y)) must recover y."""
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y_test = np.array([-2.0, 0.0, 0.5])
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cdf_vals = lognakagami.cdf(y_test, m=2.0, Omega=1.0)
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np.testing.assert_allclose(lognakagami.ppf(cdf_vals, m=2.0, Omega=1.0), y_test, atol=1e-8)
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def test_argcheck_rejects_m_below_half(self):
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"""m < 0.5 must not produce a valid (positive-finite) PDF value."""
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val = lognakagami.pdf(0.0, m=0.3, Omega=1.0)
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assert not (np.isfinite(val) and val > 0)
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def test_argcheck_rejects_non_positive_omega(self):
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"""Omega <= 0 must not produce a valid (positive-finite) PDF value."""
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val = lognakagami.pdf(0.0, m=2.0, Omega=-1.0)
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assert not (np.isfinite(val) and val > 0)
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def test_stats_mean(self):
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"""Analytical mean must equal 0.5 * (digamma(m) - log(m) + log(Omega))."""
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m, Omega = 3.0, 2.0
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expected_mean = 0.5 * (sc.digamma(m) - np.log(m) + np.log(Omega))
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dist_mean = float(lognakagami.stats(m=m, Omega=Omega, moments="m"))
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assert pytest.approx(dist_mean, rel=1e-10) == expected_mean
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def test_stats_mean_omega_shifts_by_half_log_omega(self):
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"""Changing Omega shifts the mean by 0.5*log(Omega) and leaves variance unchanged."""
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m = 2.0
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mean1 = float(lognakagami.stats(m=m, Omega=1.0, moments="m"))
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mean4 = float(lognakagami.stats(m=m, Omega=4.0, moments="m"))
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assert pytest.approx(mean4 - mean1, rel=1e-10) == 0.5 * np.log(4.0)
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def test_stats_variance_independent_of_omega(self):
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"""Variance must equal 0.25 * polygamma(1, m) and not depend on Omega."""
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m = 3.0
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expected_var = 0.25 * sc.polygamma(1, m)
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for Omega in [0.5, 1.0, 4.0]:
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_, dist_var, *_ = lognakagami.stats(m=m, Omega=Omega, moments="mv")
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assert pytest.approx(float(dist_var), rel=1e-10) == expected_var
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def test_rvs_samples_are_finite(self):
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"""Random samples must be finite real numbers."""
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rng = np.random.default_rng(42)
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samples = lognakagami.rvs(m=2.0, Omega=1.0, size=200, random_state=rng)
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assert samples.shape == (200,)
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assert np.all(np.isfinite(samples))
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def test_rvs_sample_mean_near_expected(self):
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"""Sample mean of many RVS should be close to the distribution mean."""
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m, Omega = 2.0, 3.0
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rng = np.random.default_rng(0)
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samples = lognakagami.rvs(m=m, Omega=Omega, size=50_000, random_state=rng)
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expected_mean = float(lognakagami.stats(m=m, Omega=Omega, moments="m"))
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assert pytest.approx(samples.mean(), rel=5e-2) == expected_mean
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# ── loggamma_dist unit tests ──────────────────────────────────────────────────
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class TestLogGamma:
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def test_pdf_is_positive_on_real_line(self):
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"""PDF must be strictly positive for all real y and a > 0."""
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vals = loggamma_dist.pdf(Y, a=2.0)
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assert np.all(vals > 0)
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def test_pdf_integrates_to_one(self):
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"""Numerical integral of PDF over the real line should be ≈ 1."""
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y_fine = np.linspace(-30, 10, 200_000)
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integral = np.trapezoid(loggamma_dist.pdf(y_fine, a=2.0), y_fine)
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assert pytest.approx(integral, abs=1e-3) == 1.0
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def test_logpdf_equals_log_pdf(self):
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"""logpdf must equal log(pdf) for numerical consistency."""
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log_via_pdf = np.log(loggamma_dist.pdf(Y, a=2.0))
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log_direct = loggamma_dist.logpdf(Y, a=2.0)
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np.testing.assert_allclose(log_direct, log_via_pdf, rtol=1e-6)
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def test_cdf_is_monotone_increasing(self):
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"""CDF must be strictly non-decreasing."""
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cdf_vals = loggamma_dist.cdf(Y, a=2.0)
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assert np.all(np.diff(cdf_vals) >= 0)
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def test_cdf_and_sf_sum_to_one(self):
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"""CDF + SF must equal 1 at every point."""
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cdf_vals = loggamma_dist.cdf(Y, a=2.0)
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sf_vals = loggamma_dist.sf(Y, a=2.0)
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np.testing.assert_allclose(cdf_vals + sf_vals, 1.0, atol=1e-12)
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def test_ppf_inverts_cdf(self):
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"""ppf(cdf(y)) must recover y."""
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y_test = np.array([-2.0, 0.0, 1.0])
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cdf_vals = loggamma_dist.cdf(y_test, a=2.0)
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np.testing.assert_allclose(loggamma_dist.ppf(cdf_vals, a=2.0), y_test, atol=1e-8)
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def test_argcheck_rejects_non_positive_a(self):
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"""a <= 0 must not produce a valid (positive-finite) PDF value."""
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val = loggamma_dist.pdf(0.0, a=-1.0)
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assert not (np.isfinite(val) and val > 0)
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def test_stats_mean_equals_digamma(self):
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"""Analytical mean must equal digamma(a)."""
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a = 3.0
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expected_mean = sc.digamma(a)
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dist_mean = float(loggamma_dist.stats(a=a, moments="m"))
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assert pytest.approx(dist_mean, rel=1e-10) == expected_mean
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def test_stats_variance_equals_trigamma(self):
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"""Analytical variance must equal polygamma(1, a)."""
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a = 3.0
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expected_var = sc.polygamma(1, a)
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_, dist_var, *_ = loggamma_dist.stats(a=a, moments="mv")
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assert pytest.approx(float(dist_var), rel=1e-10) == expected_var
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def test_log_transform_relation_to_gamma(self):
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"""loggamma_dist.pdf(y) must equal gamma.pdf(exp(y)) * exp(y) (change-of-variable)."""
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from scipy.stats import gamma as scipy_gamma
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y_test = np.linspace(-3.0, 3.0, 20)
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direct = loggamma_dist.pdf(y_test, a=2.0)
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via_gamma = scipy_gamma.pdf(np.exp(y_test), a=2.0) * np.exp(y_test)
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np.testing.assert_allclose(direct, via_gamma, rtol=1e-6)
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def test_rvs_samples_are_finite(self):
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"""Random samples must be finite real numbers."""
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rng = np.random.default_rng(42)
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samples = loggamma_dist.rvs(a=2.0, size=200, random_state=rng)
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assert samples.shape == (200,)
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assert np.all(np.isfinite(samples))
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def test_rvs_sample_mean_near_expected(self):
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"""Sample mean of many RVS should be close to the distribution mean."""
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a = 2.0
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rng = np.random.default_rng(0)
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samples = loggamma_dist.rvs(a=a, size=50_000, random_state=rng)
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expected_mean = float(loggamma_dist.stats(a=a, moments="m"))
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assert pytest.approx(samples.mean(), rel=5e-2) == expected_mean
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if __name__ == "__main__":
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plot_k_dist_varying_alpha()
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plot_k_dist_varying_mu()
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