feat(distributions): add logweibull, ricegamma, and logricegamma

Add three new continuous random variables for log-domain and
linear-domain clutter modeling with compound Gamma-Rice structure.

Fix numerical stability of k_dist._logpdf and logk._log_kve via a
three-regime log(kve) asymptotic (direct / large-z Hankel / large-order
Gamma); replace quad-based k_dist._cdf with Gauss-Laguerre quadrature.

Fix fitter: use np.asarray instead of np.abs in fit(), pass fit_params
to goodness_of_fit so the observed-data statistic reuses fitted params.
Skip non-finite quantiles in QQ plots. Add plot_qq_plots_sns(); rename
histogram_with_fits_seaborn() to histogram_with_fits_sns(). Add unit
tests for logweibull and logricegamma.

etc/fitting/fitter.py

@@ -8,6 +8,12 @@ from scipy.stats import rv_continuous, goodness_of_fit
 from plotly.subplots import make_subplots
 
 
+def set_plot_style():
+    sns.set_style("whitegrid")
+    sns.set_context("paper", font_scale=1.25)
+
+
+
 @dataclass
 class DistributionSummary:
     """
@@ -181,7 +187,7 @@ class Fitter:
             Mapping of distribution name → summary (test_result is None
             until validate() is called).
         """
-        data_flat = np.abs(data).flatten()
+        data_flat = np.asarray(data).flatten()
         self._last_data_flat = data_flat
 
         for dist in self.dist_list:
@@ -213,8 +219,16 @@ class Fitter:
         data_flat = self._last_data_flat
         for dist in self.dist_list:
             _summary = self._dist[dist.name]
+            # Build fit_params dict so goodness_of_fit reuses the already-fitted
+            # parameters for the observed-data statistic instead of re-fitting.
+            shape_names = [s.strip() for s in dist.shapes.split(',')] if dist.shapes else []
+            all_param_names = shape_names + ['loc', 'scale']
+            fit_params_dict = dict(zip(all_param_names, _summary.fit_result_params))
             test_result = goodness_of_fit(
-                dist, data_flat, statistic=_summary.statistic_method, **kwargs
+                dist, data_flat,
+                statistic=_summary.statistic_method,
+                fit_params=fit_params_dict,
+                **kwargs,
             )
             _summary.test_result = test_result
             self._dist[dist.name] = _summary
@@ -276,13 +290,21 @@ class Fitter:
                 plotting_positions, *summary.fit_result_params
             )
 
+            # Drop NaN/inf quantiles that arise when ppf fails to converge
+            valid = np.isfinite(theoretical_quantiles)
+            if not valid.any():
+                print(f"Distribution '{dist_name}': all theoretical quantiles are non-finite. Skipping QQ plot.")
+                continue
+            theoretical_quantiles = theoretical_quantiles[valid]
+            sorted_data_plot = sorted_data[valid]
+
             # Create QQ plot in each subplot
             row = (list(self._dist.keys()).index(dist_name) // num_cols) + 1
             col = (list(self._dist.keys()).index(dist_name) % num_cols) + 1
             fig.add_trace(
                 go.Scatter(
                     x=theoretical_quantiles,
-                    y=sorted_data,
+                    y=sorted_data_plot,
                     mode="markers",
                     name=dist_name,
                 ),
@@ -290,8 +312,8 @@ class Fitter:
                 col=col,
             )
             # Add a reference line y=x
-            min_val = min(theoretical_quantiles.min(), sorted_data.min())
+            min_val = min(theoretical_quantiles.min(), sorted_data_plot.min())
-            max_val = max(theoretical_quantiles.max(), sorted_data.max())
+            max_val = max(theoretical_quantiles.max(), sorted_data_plot.max())
             fig.add_trace(
                 go.Scatter(
                     x=[min_val, max_val],
@@ -322,6 +344,88 @@ class Fitter:
             showlegend=False,
             autosize=True,
         )
+    
+        return fig
+
+    def plot_qq_plots_sns(self, method: str = "hazen"):
+        """
+        Generate QQ plots for each fitted distribution using seaborn/matplotlib.
+
+        Parameters
+        ----------
+        method : str
+            Plotting positions formula. Either 'hazen' (default) or 'filliben'.
+        """
+        if not hasattr(self, "_last_data_flat"):
+            raise RuntimeError("No data available. Call fit() first.")
+        if method not in ("hazen", "filliben"):
+            raise ValueError(f"method must be 'hazen' or 'filliben', got '{method}'.")
+
+        set_plot_style()
+
+        dist_names = list(self._dist.keys())
+        num_dists = len(dist_names)
+        num_cols = 2
+        num_rows = (num_dists + 1) // 2
+
+        dot_color = sns.color_palette()[0]
+
+        fig, axes = plt.subplots(num_rows, num_cols, figsize=(6 * num_cols, 5 * num_rows))
+        axes = np.array(axes).flatten()
+
+        sorted_data = np.sort(self._last_data_flat)
+        n = len(sorted_data)
+        i = np.arange(1, n + 1)
+        if method == "hazen":
+            plotting_positions = (i - 0.5) / n
+        else:
+            plotting_positions = (i - 0.3175) / (n + 0.365)
+            plotting_positions[0] = 1 - 0.5 ** (1 / n)
+            plotting_positions[-1] = 0.5 ** (1 / n)
+
+        for idx, (dist_name, summary) in enumerate(self):
+            ax = axes[idx]
+            if summary.test_result is None:
+                ax.set_title(dist_name)
+                ax.text(0.5, 0.5, "Not validated", ha="center", va="center",
+                        transform=ax.transAxes)
+                continue
+
+            theoretical_quantiles = summary.distribution_object.ppf(
+                plotting_positions, *summary.fit_result_params
+            )
+            valid = np.isfinite(theoretical_quantiles)
+            if not valid.any():
+                ax.set_title(dist_name)
+                ax.text(0.5, 0.5, "All quantiles non-finite", ha="center", va="center",
+                        transform=ax.transAxes)
+                continue
+
+            tq = theoretical_quantiles[valid]
+            sd = sorted_data[valid]
+
+            ax.scatter(tq, sd, color=dot_color, s=8, alpha=0.6, linewidths=0)
+            ref_min = min(tq.min(), sd.min())
+            ref_max = max(tq.max(), sd.max())
+            ax.plot([ref_min, ref_max], [ref_min, ref_max], "k--", linewidth=1)
+
+            pvalue = summary.pvalue
+            stat_color = "green" if pvalue > 0.05 else "red"
+            ax.text(0.95, 0.05,
+                    f"{summary.statistic_method}={summary.gof_statistic:.4f}",
+                    transform=ax.transAxes, ha="right", va="bottom",
+                    fontsize=9, color=stat_color)
+
+            ax.set_title(dist_name)
+            ax.set_xlabel("Theoretical Quantiles")
+            ax.set_ylabel("Empirical Quantiles")
+
+        # Hide unused axes
+        for idx in range(num_dists, len(axes)):
+            axes[idx].set_visible(False)
+
+        fig.suptitle(f"QQ Plots of Fitted Distributions ({method})", y=1.01)
+        plt.tight_layout()
         return fig
 
     def histogram_with_fits(self):
@@ -389,7 +493,7 @@ class Fitter:
 
         return fig
 
-    def histogram_with_fits_seaborn(self):
+    def histogram_with_fits_sns(self):
         """
         Generate a histogram of the data with overlaid PDFs of each fitted distribution using seaborn.
         Requires that fit() has been called to populate parameters.
@@ -422,7 +526,7 @@ class Fitter:
             ax.plot(
                 x,
                 pdf_values,
-                label=f"{summary.distribution_name} --- p={summary.pvalue:.4f}",
+                label=f"{summary.distribution_name}",
             )
         # put title in top left, make it smaller, change it font to sans and put in light gray
         ax.set_title(

etc/tests/test_distributions.py

@@ -7,7 +7,7 @@ import os
 
 sys.path.insert(0, os.path.join(os.path.dirname(__file__), ".."))
 
-from tools.distributions import k_dist, logk, lognakagami, loggamma_dist, lograyleigh, logrice
+from tools.distributions import k_dist, logk, lognakagami, loggamma_dist, lograyleigh, logrice, logweibull, logricegamma, ricegamma
 
 
 X = np.linspace(0.01, 10.0, 500)
@@ -677,6 +677,237 @@ class TestLogK:
         np.testing.assert_allclose(pdf_ab, pdf_ba, rtol=1e-6)
 
 
+# ── logweibull unit tests ─────────────────────────────────────────────────────
+
+Y_LOGWEIBULL = np.linspace(-10.0, 10.0, 500)
+
+
+class TestLogWeibull:
+    def test_logpdf_is_finite_on_real_line(self):
+        """logpdf must be finite for all real y."""
+        vals = logweibull.logpdf(Y_LOGWEIBULL, k=2.0, lam=1.0)
+        assert np.all(np.isfinite(vals))
+
+    def test_pdf_integrates_to_one(self):
+        """Numerical integral of PDF over the real line should be ≈ 1."""
+        y_fine = np.linspace(-20.0, 20.0, 200_000)
+        integral = np.trapezoid(logweibull.pdf(y_fine, k=2.0, lam=1.0), y_fine)
+        assert pytest.approx(integral, abs=1e-3) == 1.0
+
+    def test_logpdf_equals_log_pdf(self):
+        """logpdf must equal log(pdf) at points where pdf does not underflow to zero."""
+        y_bulk = np.linspace(-10.0, 20.0, 100)
+        k, lam = 2.0, np.exp(12.0)
+        pdf_vals = logweibull.pdf(y_bulk, k=k, lam=lam)
+        mask = pdf_vals > 0
+        np.testing.assert_allclose(
+            logweibull.logpdf(y_bulk[mask], k=k, lam=lam),
+            np.log(pdf_vals[mask]),
+            rtol=1e-6,
+        )
+
+    def test_change_of_variable_matches_weibull(self):
+        """logweibull.pdf(y) must equal weibull_min.pdf(exp(y)) * exp(y)."""
+        from scipy.stats import weibull_min
+        y_test = np.linspace(-3.0, 3.0, 20)
+        k, lam = 2.0, 1.5
+        direct = logweibull.pdf(y_test, k=k, lam=lam)
+        via_w = weibull_min.pdf(np.exp(y_test), c=k, scale=lam) * np.exp(y_test)
+        np.testing.assert_allclose(direct, via_w, rtol=1e-6)
+
+    def test_cdf_is_monotone_increasing(self):
+        """CDF must be strictly non-decreasing."""
+        y_grid = np.linspace(-5.0, 5.0, 50)
+        cdf_vals = logweibull.cdf(y_grid, k=2.0, lam=1.0)
+        assert np.all(np.diff(cdf_vals) >= -1e-12)
+
+    def test_cdf_matches_weibull(self):
+        """logweibull.cdf(y) must equal weibull_min.cdf(exp(y))."""
+        from scipy.stats import weibull_min
+        y_test = np.array([-2.0, 0.0, 1.0, 2.0])
+        k, lam = 1.5, 2.0
+        np.testing.assert_allclose(
+            logweibull.cdf(y_test, k=k, lam=lam),
+            weibull_min.cdf(np.exp(y_test), c=k, scale=lam),
+            rtol=1e-6,
+        )
+
+    def test_sf_plus_cdf_equals_one(self):
+        """sf + cdf must equal 1 everywhere."""
+        y_test = np.linspace(-3.0, 3.0, 20)
+        k, lam = 2.0, 1.0
+        np.testing.assert_allclose(
+            logweibull.cdf(y_test, k=k, lam=lam) + logweibull.sf(y_test, k=k, lam=lam),
+            1.0,
+            rtol=1e-12,
+        )
+
+    def test_ppf_inverts_cdf(self):
+        """ppf must be the exact inverse of cdf: cdf(ppf(q)) == q."""
+        # Round-trip over quantiles to avoid CDF saturation at extreme y values
+        q_test = np.array([0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95])
+        k, lam = 2.0, np.exp(12.0)
+        np.testing.assert_allclose(
+            logweibull.cdf(logweibull.ppf(q_test, k=k, lam=lam), k=k, lam=lam),
+            q_test,
+            rtol=1e-8,
+        )
+
+    def test_stats_mean_shifts_by_log_lam(self):
+        """Doubling lam shifts the mean by ln(2), leaving variance unchanged."""
+        k = 2.0
+        mean1 = float(logweibull.stats(k=k, lam=1.0, moments="m"))
+        mean2 = float(logweibull.stats(k=k, lam=2.0, moments="m"))
+        assert pytest.approx(mean2 - mean1, rel=1e-10) == np.log(2.0)
+
+    def test_stats_variance_scales_with_k(self):
+        """Variance must equal psi_1(1) / k^2."""
+        for k in [0.5, 1.0, 2.0]:
+            _, var, *_ = logweibull.stats(k=k, lam=1.0, moments="mv")
+            expected = sc.polygamma(1, 1) / k ** 2
+            assert pytest.approx(float(var), rel=1e-10) == expected
+
+    def test_stats_variance_is_lam_independent(self):
+        """Variance must not depend on lam."""
+        k = 2.0
+        _, var1, *_ = logweibull.stats(k=k, lam=1.0, moments="mv")
+        _, var2, *_ = logweibull.stats(k=k, lam=5.0, moments="mv")
+        assert pytest.approx(float(var1), rel=1e-10) == float(var2)
+
+    def test_argcheck_rejects_non_positive_k(self):
+        """k <= 0 must not produce a valid PDF value."""
+        val = logweibull.pdf(0.0, k=-1.0, lam=1.0)
+        assert not (np.isfinite(val) and val > 0)
+
+    def test_argcheck_rejects_non_positive_lam(self):
+        """lam <= 0 must not produce a valid PDF value."""
+        val = logweibull.pdf(0.0, k=1.0, lam=-1.0)
+        assert not (np.isfinite(val) and val > 0)
+
+    def test_rvs_are_finite(self):
+        """Random samples must be finite real numbers."""
+        rng = np.random.default_rng(42)
+        samples = logweibull.rvs(k=2.0, lam=1.0, size=500, random_state=rng)
+        assert samples.shape == (500,)
+        assert np.all(np.isfinite(samples))
+
+    def test_rvs_sample_mean_near_analytical(self):
+        """Sample mean must be close to the analytical mean."""
+        k, lam = 2.0, 1.5
+        rng = np.random.default_rng(0)
+        samples = logweibull.rvs(k=k, lam=lam, size=100_000, random_state=rng)
+        expected_mean = float(logweibull.stats(k=k, lam=lam, moments="m"))
+        assert pytest.approx(float(samples.mean()), rel=5e-2) == expected_mean
+
+    def test_rvs_sample_variance_near_analytical(self):
+        """Sample variance must be close to the analytical variance."""
+        k, lam = 2.0, 1.5
+        rng = np.random.default_rng(1)
+        samples = logweibull.rvs(k=k, lam=lam, size=100_000, random_state=rng)
+        _, expected_var, *_ = logweibull.stats(k=k, lam=lam, moments="mv")
+        assert pytest.approx(float(np.var(samples)), rel=5e-2) == float(expected_var)
+
+
+# ── logricegamma unit tests ───────────────────────────────────────────────────
+# PDF is expensive (numerical integration per point), so grids are kept small.
+
+Y_LRICEGAMMA = np.linspace(-5.0, 5.0, 30)
+
+
+class TestLogRiceGamma:
+    def test_pdf_is_positive_for_valid_params(self):
+        """PDF must be strictly positive for finite y and valid parameters."""
+        vals = logricegamma.pdf(Y_LRICEGAMMA, alpha=2.0, beta=1.0, K=1.0)
+        assert np.all(vals > 0)
+
+    def test_pdf_integrates_to_one(self):
+        """Numerical integral of PDF over a wide domain should be ≈ 1."""
+        y_fine = np.linspace(-15.0, 10.0, 1000)
+        integral = np.trapezoid(
+            logricegamma.pdf(y_fine, alpha=2.0, beta=1.0, K=1.0), y_fine
+        )
+        assert pytest.approx(integral, abs=1e-2) == 1.0
+
+    def test_pdf_integrates_to_one_k_zero(self):
+        """Normalisation must hold for K=0 (Rice collapses to Rayleigh)."""
+        y_fine = np.linspace(-15.0, 10.0, 1000)
+        integral = np.trapezoid(
+            logricegamma.pdf(y_fine, alpha=2.0, beta=1.0, K=0.0), y_fine
+        )
+        assert pytest.approx(integral, abs=1e-2) == 1.0
+
+    def test_pdf_integrates_to_one_large_K(self):
+        """Normalisation must hold for large K (highly specular regime)."""
+        y_fine = np.linspace(-10.0, 15.0, 1000)
+        integral = np.trapezoid(
+            logricegamma.pdf(y_fine, alpha=2.0, beta=1.0, K=10.0), y_fine
+        )
+        assert pytest.approx(integral, abs=1e-2) == 1.0
+
+    def test_logpdf_equals_log_pdf(self):
+        """logpdf must equal log(pdf) where pdf does not underflow."""
+        y_bulk = np.linspace(-3.0, 3.0, 15)
+        pdf_vals = logricegamma.pdf(y_bulk, alpha=2.0, beta=1.0, K=1.0)
+        mask = pdf_vals > 0
+        np.testing.assert_allclose(
+            logricegamma.logpdf(y_bulk[mask], alpha=2.0, beta=1.0, K=1.0),
+            np.log(pdf_vals[mask]),
+            rtol=1e-6,
+        )
+
+    def test_argcheck_rejects_non_positive_alpha(self):
+        """alpha <= 0 must not produce a valid PDF value."""
+        val = logricegamma.pdf(0.0, alpha=-1.0, beta=1.0, K=1.0)
+        assert not (np.isfinite(val) and val > 0)
+
+    def test_argcheck_rejects_non_positive_beta(self):
+        """beta <= 0 must not produce a valid PDF value."""
+        val = logricegamma.pdf(0.0, alpha=2.0, beta=-1.0, K=1.0)
+        assert not (np.isfinite(val) and val > 0)
+
+    def test_argcheck_rejects_negative_K(self):
+        """K < 0 must not produce a valid PDF value."""
+        val = logricegamma.pdf(0.0, alpha=2.0, beta=1.0, K=-1.0)
+        assert not (np.isfinite(val) and val > 0)
+
+    def test_cdf_is_monotone_increasing(self):
+        """CDF must be strictly non-decreasing."""
+        y_grid = np.linspace(-4.0, 4.0, 15)
+        cdf_vals = logricegamma.cdf(y_grid, alpha=2.0, beta=1.0, K=1.0)
+        assert np.all(np.diff(cdf_vals) >= -1e-10)
+
+    def test_rvs_samples_are_finite(self):
+        """Random samples must be finite real numbers."""
+        rng = np.random.default_rng(42)
+        samples = logricegamma.rvs(alpha=2.0, beta=1.0, K=1.0, size=500, random_state=rng)
+        assert samples.shape == (500,)
+        assert np.all(np.isfinite(samples))
+
+    def test_rvs_second_moment_equals_alpha_times_beta(self):
+        """E[exp(2Y)] = E[X²] must equal alpha*beta (total average power from docstring)."""
+        alpha, beta, K = 2.0, 1.5, 2.0
+        rng = np.random.default_rng(0)
+        samples = logricegamma.rvs(alpha=alpha, beta=beta, K=K, size=100_000, random_state=rng)
+        assert pytest.approx(float(np.mean(np.exp(2.0 * samples))), rel=5e-2) == alpha * beta
+
+    def test_rvs_second_moment_k_zero(self):
+        """E[X²] = alpha*beta must hold for K=0."""
+        alpha, beta, K = 3.0, 0.5, 0.0
+        rng = np.random.default_rng(1)
+        samples = logricegamma.rvs(alpha=alpha, beta=beta, K=K, size=100_000, random_state=rng)
+        assert pytest.approx(float(np.mean(np.exp(2.0 * samples))), rel=5e-2) == alpha * beta
+
+    def test_rvs_sample_mean_consistent_with_pdf(self):
+        """Sample mean from RVS should match the numerically integrated mean from the PDF."""
+        alpha, beta, K = 2.0, 1.0, 1.0
+        rng = np.random.default_rng(2)
+        samples = logricegamma.rvs(alpha=alpha, beta=beta, K=K, size=50_000, random_state=rng)
+        y_fine = np.linspace(-15.0, 10.0, 1000)
+        pdf_vals = logricegamma.pdf(y_fine, alpha=alpha, beta=beta, K=K)
+        numerical_mean = float(np.trapezoid(y_fine * pdf_vals, y_fine))
+        assert pytest.approx(float(samples.mean()), rel=1e-1) == numerical_mean
+
+
 if __name__ == "__main__":
     plot_k_dist_varying_alpha()
     plot_k_dist_varying_mu()

etc/tools/distributions.py

@@ -161,11 +161,25 @@ Priority order for overriding to improve tail accuracy:
 
 from scipy.stats import rv_continuous, ncx2
 from scipy.special import kve, gammaln
-from scipy.integrate import quad
 import scipy.special as sc
 from scipy.stats._distn_infrastructure import _ShapeInfo
 import numpy as np
 
+# Gauss-Legendre nodes/weights on [-1, 1] — used by logricegamma_gen._batch_integral.
+# Computed once at import time; 200 nodes give machine-precision accuracy for smooth,
+# well-resolved integrands while keeping the (N, 200) batch cost negligible.
+_GL_M = 200
+_gl_xi, _gl_wi = np.polynomial.legendre.leggauss(_GL_M)
+
+# Gauss-Hermite nodes/weights — used by k_dist._cdf for the large-beta branch.
+# When beta > _BETA_GH_THRESH, Gamma(β,1) weights overflow float64 (Γ(β) → ∞).
+# We instead approximate E_{t~Gamma(β,1)}[f(t)] via the Normal approximation:
+#   Gamma(β,1) ≈ Normal(β, √β)  =>  E[f(t)] ≈ (1/√π) Σ_k w_k f(β + √(2β)·u_k)
+_GH_M = 30
+_gh_nodes, _gh_weights = np.polynomial.hermite.hermgauss(_GH_M)
+_gh_weights_norm = _gh_weights / np.sqrt(np.pi)   # unit-mass weights
+_BETA_GH_THRESH = 150.0
+
 
 class k_gen(rv_continuous):
     """Generalized K distribution for radar clutter modeling.
@@ -198,6 +212,43 @@ class k_gen(rv_continuous):
     def _pdf(self, x, mu, alpha, beta):
         return np.exp(self._logpdf(x, mu, alpha, beta))
 
+    @staticmethod
+    def _log_kve_stable(v, z):
+        """Numerically stable log(kve(v, z)) = log(K_v(z)) + z.
+
+        Three regimes:
+        - direct:      kve(v, z) > 0 (no over/underflow)
+        - large-z:     z >> |v|  — Hankel 2-term asymptotic
+        - large-order: |v| >> z  — leading Gamma asymptotic
+                       log(K_v(z)) ≈ gammaln(|v|) + |v|*log(2/z) - log(2)
+        """
+        z = np.asarray(z, dtype=float)
+        v = np.asarray(v, dtype=float)
+        abs_v = np.abs(v)
+        kve_val = kve(v, z)
+        z_safe = np.where(z > 0, z, 1.0)
+        # Large-z Hankel asymptotic (accurate when z >> |v|)
+        mu_v = 4.0 * v ** 2
+        # Clip log1p argument to (-1, inf) to avoid domain errors when np.where
+        # evaluates this branch even for points where it won't be selected.
+        log1p_arg = np.maximum(
+            (mu_v - 1.0) / (8.0 * z_safe)
+            + (mu_v - 1.0) * (mu_v - 9.0) / (128.0 * z_safe ** 2),
+            -1.0 + 1e-15,
+        )
+        log_asymp_largez = (
+            0.5 * (np.log(np.pi) - np.log(2.0) - np.log(z_safe))
+            + np.log1p(log1p_arg)
+        )
+        # Large-order asymptotic (accurate when |v| >> z > 0)
+        # log(kve(v,z)) = log(K_v(z)) + z ≈ gammaln(|v|) + |v|*log(2/z) - log(2) + z
+        log_asymp_largev = gammaln(abs_v) + abs_v * np.log(2.0 / z_safe) - np.log(2.0) + z
+        # kve overflows to +inf when |v|>>z, underflows to 0 when z>>|v|
+        kve_bad = ~np.isfinite(kve_val) | (kve_val <= 0)
+        use_largev = (abs_v > z_safe + 2.0) & kve_bad
+        log_asymp = np.where(use_largev, log_asymp_largev, log_asymp_largez)
+        return np.where(kve_bad, log_asymp, np.log(kve_val))
+
     def _logpdf(self, x, mu, alpha, beta):
         half_sum = (alpha + beta) / 2.0
         log_ab_over_mu = np.log(alpha) + np.log(beta) - np.log(mu)
@@ -208,7 +259,7 @@ class k_gen(rv_continuous):
             - gammaln(beta)
             + half_sum * log_ab_over_mu
             + (half_sum - 1.0) * np.log(x)
-            + np.log(kve(alpha - beta, z))
+            + self._log_kve_stable(alpha - beta, z)
             - z
         )
 
@@ -235,18 +286,53 @@ class k_gen(rv_continuous):
         return mean, variance, skewness, kurtosis
 
     def _cdf(self, x, mu, alpha, beta):
-        # scipy broadcasts params to match x's shape before calling _cdf,
+        # K-distribution CDF via the compound-Gamma representation:
-        # so mu/alpha/beta may be arrays. Pass all four to np.vectorize so
+        #   X = Gamma(alpha, tau/alpha),  tau ~ Gamma(beta, mu/beta)
-        # each argument arrives as a scalar inside _scalar.
+        # => F(x) = (1/Γ(β)) ∫_0^∞ gammainc(α, xαβ/(μt)) t^{β-1} e^{-t} dt
-        # Substitution u = sqrt(x) regularises the integrand near u=0:
+        #
-        # f(u²)*2u ~ u^(alpha+beta-1), smooth for alpha,beta > 0.
+        # For β ≤ _BETA_GH_THRESH: (β−1)-order Gauss-Laguerre quadrature.
+        # For β > _BETA_GH_THRESH: Gamma(β,1) ≈ Normal(β,√β), so we switch to
+        #   Gauss-Hermite:  E[f(t)] ≈ (1/√π) Σ_k w_k f(β + √(2β)·u_k).
+        from scipy.special import gammainc, roots_genlaguerre
+        from scipy.special import gamma as sp_gamma
+
+        x = np.asarray(x, dtype=float)
+        mu = np.asarray(mu, dtype=float)
+        alpha = np.asarray(alpha, dtype=float)
+        beta = np.asarray(beta, dtype=float)
+
+        _N_PTS = 50
+
+        def _gh_branch(x_, alpha_, mu_, bi):
+            """Gauss-Hermite CDF for large beta (Normal approx to Gamma(β,1))."""
+            t_gh = bi + np.sqrt(2.0 * bi) * _gh_nodes        # shape (GH_M,)
+            t_gh = np.maximum(t_gh, 1e-10)
+            t_args = (x_ * alpha_ / mu_)[..., np.newaxis] * (bi / t_gh)
+            probs = gammainc(alpha_[..., np.newaxis], t_args)
+            return np.dot(probs, _gh_weights_norm)
+
+        # Fast path: beta is uniform across all inputs (the common case in fit).
+        beta_vals = np.unique(beta)
+        if beta_vals.size == 1:
+            bi = float(beta_vals[0])
+            if bi > _BETA_GH_THRESH:
+                return _gh_branch(x, alpha, mu, bi)
+            nodes, weights = roots_genlaguerre(_N_PTS, bi - 1.0)
+            t_args = (x * alpha / mu)[..., np.newaxis] * (bi / nodes)
+            probs = gammainc(alpha[..., np.newaxis], t_args)
+            return np.dot(probs, weights) / sp_gamma(bi)
+
+        # Slow path: heterogeneous beta — fall back to per-element loop.
         def _scalar(xi, mui, ai, bi):
-            val, _ = quad(
+            bi = float(bi)
-                lambda u: float(self._pdf(float(u * u), float(mui), float(ai), float(bi))) * 2.0 * u,
+            xi_, ai_, mui_ = np.asarray([float(xi)]), np.asarray([float(ai)]), float(mui)
-                0.0, float(np.sqrt(xi)),
+            if bi > _BETA_GH_THRESH:
-                limit=200, epsabs=1.49e-10, epsrel=1.49e-8,
+                return float(_gh_branch(xi_, ai_, np.asarray([mui_]), bi)[0])
-            )
+            nodes, weights = roots_genlaguerre(_N_PTS, bi - 1.0)
-            return val
+            t_args = float(xi) * float(ai) * bi / (float(mui) * nodes)
+            probs = gammainc(float(ai), t_args)
+            return float(np.dot(probs, weights) / sp_gamma(bi))
+
         return np.vectorize(_scalar)(x, mu, alpha, beta)
 
     def _rvs(self, mu, alpha, beta, size=None, random_state=None):
@@ -300,27 +386,40 @@ class logk_gen(rv_continuous):
 
     @staticmethod
     def _log_kve(v, z):
-        """log(kve(v, z)) = log(Kv(z)) + z, stable for all z > 0.
+        """Numerically stable log(kve(v, z)) = log(K_v(z)) + z.
 
-        For large z, kve(v, z) ≈ sqrt(π/(2z)) underflows to 0 in float64,
+        Three regimes:
-        making log(kve) return -inf/-nan.  The asymptotic expansion:
+        - direct:      kve(v, z) > 0 (no over/underflow)
-
+        - large-z:     z >> |v|  — Hankel 2-term asymptotic
-            log(kve(v,z)) ≈ 0.5*log(π/(2z)) + log1p((4v²-1)/(8z) +
+        - large-order: |v| >> z  — leading Gamma asymptotic
-                             (4v²-1)(4v²-9)/(128z²))
+                       log(K_v(z)) ≈ gammaln(|v|) + |v|*log(2/z) - log(2)
-
-        is used whenever the direct evaluation would underflow.
         """
         z = np.asarray(z, dtype=float)
         v = np.asarray(v, dtype=float)
+        abs_v = np.abs(v)
         kve_val = kve(v, z)
-        # Asymptotic (2-term Hankel expansion) — accurate to O(z^{-3})
+        z_safe = np.where(z > 0, z, 1.0)
+        # Large-z Hankel asymptotic (accurate when z >> |v|)
         mu_v = 4.0 * v ** 2
-        log_asymp = (
+        # Clip log1p argument to (-1, inf) to avoid domain errors when np.where
-            0.5 * (np.log(np.pi) - np.log(2.0) - np.log(np.where(z > 0, z, 1.0)))
+        # evaluates this branch even for points where it won't be selected.
-            + np.log1p((mu_v - 1.0) / (8.0 * np.where(z > 0, z, 1.0))
+        log1p_arg = np.maximum(
-                       + (mu_v - 1.0) * (mu_v - 9.0) / (128.0 * np.where(z > 0, z**2, 1.0)))
+            (mu_v - 1.0) / (8.0 * z_safe)
+            + (mu_v - 1.0) * (mu_v - 9.0) / (128.0 * z_safe ** 2),
+            -1.0 + 1e-15,
         )
-        return np.where(kve_val > 0, np.log(np.where(kve_val > 0, kve_val, 1.0)), log_asymp)
+        log_asymp_largez = (
+            0.5 * (np.log(np.pi) - np.log(2.0) - np.log(z_safe))
+            + np.log1p(log1p_arg)
+        )
+        # Large-order asymptotic (accurate when |v| >> z > 0)
+        # log(kve(v,z)) = log(K_v(z)) + z ≈ gammaln(|v|) + |v|*log(2/z) - log(2) + z
+        log_asymp_largev = gammaln(abs_v) + abs_v * np.log(2.0 / z_safe) - np.log(2.0) + z
+        # kve overflows to +inf when |v|>>z, underflows to 0 when z>>|v|
+        kve_bad = ~np.isfinite(kve_val) | (kve_val <= 0)
+        use_largev = (abs_v > z_safe + 2.0) & kve_bad
+        log_asymp = np.where(use_largev, log_asymp_largev, log_asymp_largez)
+        return np.where(kve_bad, log_asymp, np.log(kve_val))
 
     def _pdf(self, y, mu, alpha, beta):
         return np.exp(self._logpdf(y, mu, alpha, beta))
@@ -347,33 +446,158 @@ class logk_gen(rv_continuous):
         return mean, var, g1, g2
 
     def _cdf(self, y, mu, alpha, beta):
-        return k_dist.cdf(np.exp(y), mu, alpha, beta)
+        # Clip y to avoid exp() overflow (float64 max ≈ exp(709.78)).
+        # For y > 709 the CDF is indistinguishable from 1.0.
+        y_clipped = np.minimum(y, 709.0)
+        return k_dist.cdf(np.exp(y_clipped), mu, alpha, beta)
+
+    def _ppf(self, q, mu, alpha, beta):
+        # Invert via the linear-domain ppf: Y = ln(X), X ~ K(mu, alpha, beta).
+        # k_dist.ppf has a finite lower bound (a=0) so its bracket search is
+        # well-defined, avoiding the exp-overflow problem in the default logk ppf.
+        x = k_dist.ppf(q, mu, alpha, beta)
+        return np.log(np.maximum(x, np.finfo(float).tiny))
 
     def _rvs(self, mu, alpha, beta, size=None, random_state=None):
+        # Compound Gamma: tau ~ Gamma(beta, mu/beta), X|tau ~ Gamma(alpha, tau/alpha)
+        # Y = ln(X), avoids the ppf -> k_dist.ppf -> quad-CDF chain.
         tau = random_state.gamma(beta, mu / beta, size=size)
-        sample = random_state.gamma(alpha, tau / alpha)
+        x = random_state.gamma(alpha, tau / alpha)
-        return np.log(np.clip(sample, np.finfo(float).tiny, None))
+        return np.log(np.maximum(x, np.finfo(float).tiny))
+
+    def _sf(self, y, mu, alpha, beta):
+        y_clipped = np.minimum(y, 709.0)
+        return k_dist.sf(np.exp(y_clipped), mu, alpha, beta)
+
+    def _fitstart(self, data, args=None):
+        # Symmetric method-of-moments starting point using the first two cumulants:
+        #   E[Y]   = ln(mu) - ln(alpha) - ln(beta) + psi(alpha) + psi(beta)
+        #   Var[Y] = psi_1(alpha) + psi_1(beta)
+        # Symmetric start (alpha=beta): psi_1(a) ≈ 1/a  =>  a ≈ 2/Var
+        mean_d = float(np.mean(data))
+        var_d  = max(float(np.var(data)), 1e-6)
+        alpha0 = float(np.clip(2.0 / var_d, 0.5, 50.0))
+        beta0  = alpha0
+        mu0 = float(np.exp(
+            mean_d
+            + np.log(alpha0) + np.log(beta0)
+            - sc.digamma(alpha0) - sc.digamma(beta0)
+        ))
+        return (mu0, alpha0, beta0, 0.0, 1.0)
 
     def fit(self, data, *args, **kwds):
-        if ("loc" in kwds and kwds["loc"] != 0.0) or ("floc" in kwds and kwds["floc"] != 0.0):
+        """MLE fit with bounded shape parameters; loc and scale are free by default.
-            raise ValueError("logk uses a fixed loc=0.")
+
-        if ("scale" in kwds and kwds["scale"] != 1.0) or ("fscale" in kwds and kwds["fscale"] != 1.0):
+        Optimises in log-parameter space via L-BFGS-B to keep mu, alpha, beta
-            raise ValueError("logk uses a fixed scale=1.")
+        and scale strictly positive.
-        kwds.pop("loc", None)
+
-        kwds.pop("scale", None)
+        The K-distribution log-likelihood is unbounded when alpha or beta grows
-        # Supply data-driven initial guesses when none are provided so the
+        without limit, so the search is capped at _MAX.  Three starting points
-        # optimizer starts close to the data instead of the default (1,1,1).
+        are tried — one symmetric (alpha=beta from variance matching) and two
-        # E[Y] = ln(mu) + ln(alpha) + ln(beta) - digamma(alpha) - digamma(beta)
+        asymmetric (one with alpha>>beta and its mirror) — to escape the
-        # => mu0 = exp(mean(data) + ln(a0) + ln(b0) - psi(a0) - psi(b0))
+        symmetric local maximum when the data is skewed.
-        if not args:
+
-            alpha0, beta0 = 1.0, 1.0
+        loc/scale can be pinned by passing floc=0, fscale=1 as keyword args.
-            mu0 = float(np.exp(
+        """
-                np.mean(data)
+        from scipy.optimize import minimize, brentq
-                + np.log(alpha0) + np.log(beta0)
+
-                - sc.digamma(alpha0) - sc.digamma(beta0)
+        # Respect user-supplied fixed values; None means "free to optimise".
+        floc   = kwds.pop('floc',   None)
+        fscale = kwds.pop('fscale', None)
+        for k in ('loc', 'scale'):
+            kwds.pop(k, None)
+        data = np.asarray(data, dtype=float).ravel()
+
+        # Upper bound: prevents the degenerate alpha→∞ (or beta→∞) regime.
+        _MAX = 50.0
+
+        # ── symmetric starting point ──────────────────────────────────────────
+        start  = self._fitstart(data)
+        mu0    = max(float(args[0]) if len(args) > 0 else start[0], 1e-12)
+        alpha0 = float(np.clip(args[1] if len(args) > 1 else start[1], 0.01, _MAX))
+        beta0  = float(np.clip(args[2] if len(args) > 2 else start[2], 0.01, _MAX))
+
+        # ── asymmetric starting point (all variance in beta, large alpha) ─────
+        mean_d = float(np.mean(data))
+        var_d  = max(float(np.var(data)), 1e-6)
+        try:
+            beta_asym = float(brentq(
+                lambda b: sc.polygamma(1, b) - var_d, 0.05, 500.0, xtol=1e-8
             ))
-            args = (mu0, alpha0, beta0)
+        except Exception:
-        return super().fit(data, *args, floc=0.0, fscale=1.0, **kwds)
+            beta_asym = beta0
+        alpha_asym = float(np.clip(5.0 * beta_asym, 1.0, _MAX))
+        beta_asym  = float(np.clip(beta_asym, 0.01, _MAX))
+        mu_asym = float(np.exp(
+            mean_d
+            + np.log(alpha_asym) + np.log(beta_asym)
+            - sc.digamma(alpha_asym) - sc.digamma(beta_asym)
+        ))
+
+        # Starting values for loc / scale (used when free)
+        loc0   = float(floc)   if floc   is not None else 0.0
+        scale0 = float(fscale) if fscale is not None else 1.0
+
+        # ── parameter packing ─────────────────────────────────────────────────
+        # Vector layout: [log(mu), log(alpha), log(beta), loc?, log(scale)?]
+        # Slots for loc/scale are only present when they are free.
+        def pack(mu, alpha, beta):
+            v = [np.log(mu), np.log(alpha), np.log(beta)]
+            if floc   is None: v.append(loc0)
+            if fscale is None: v.append(np.log(scale0))
+            return v
+
+        def unpack(v):
+            mu = np.exp(v[0]); alpha = np.exp(v[1]); beta = np.exp(v[2])
+            idx = 3
+            if floc is None:
+                loc = float(v[idx]); idx += 1
+            else:
+                loc = float(floc)
+            scale = float(np.exp(v[idx])) if fscale is None else float(fscale)
+            return mu, alpha, beta, loc, scale
+
+        bounds = [
+            (None, None),                            # log(mu)
+            (np.log(0.01), np.log(_MAX)),             # log(alpha)
+            (np.log(0.01), np.log(_MAX)),             # log(beta)
+        ]
+        if floc   is None: bounds.append((None, None))                   # loc
+        if fscale is None: bounds.append((np.log(1e-4), np.log(100.0)))  # log(scale)
+
+        def neg_ll(v):
+            mu, alpha, beta, loc, scale = unpack(v)
+            with np.errstate(all='ignore'):
+                ll = np.sum(self.logpdf(data, mu, alpha, beta, loc=loc, scale=scale))
+            return -ll if np.isfinite(ll) else 1e15
+
+        # Candidate starting vectors: symmetric + two asymmetric (α>>β and β>>α)
+        x0_candidates = [
+            pack(mu0,    alpha0,    beta0),
+            pack(mu_asym, alpha_asym, beta_asym),
+            pack(mu_asym, beta_asym,  alpha_asym),
+        ]
+
+        best_res = None
+        best_nll = np.inf
+        with np.errstate(all='ignore'):
+            for x0 in x0_candidates:
+                x0_safe = list(x0)
+                x0_safe[1] = float(np.clip(x0_safe[1], bounds[1][0], bounds[1][1]))
+                x0_safe[2] = float(np.clip(x0_safe[2], bounds[2][0], bounds[2][1]))
+                res = minimize(
+                    neg_ll,
+                    x0=x0_safe,
+                    method='L-BFGS-B',
+                    bounds=bounds,
+                    options={'ftol': 1e-12, 'gtol': 1e-8, 'maxiter': 2000},
+                )
+                if res.fun < best_nll:
+                    best_nll = res.fun
+                    best_res = res
+
+        mu_hat, alpha_hat, beta_hat, loc_hat, scale_hat = unpack(best_res.x)
+        return (mu_hat, alpha_hat, beta_hat, loc_hat, scale_hat)
 
 
 logk = logk_gen(name="logk", shapes="mu, alpha, beta")
@@ -708,3 +932,394 @@ class logrice_gen(rv_continuous):
 
 
 logrice = logrice_gen(name='logrice', shapes="nu, sigma")
+
+
+class logweibull_gen(rv_continuous):
+    """Log-Weibull continuous random variable.
+
+    Y = ln(X) where X ~ Weibull(k, lam). The PDF is:
+
+        f(y; k, lam) = (k/lam) * (e^y/lam)^(k-1) * exp(-(e^y/lam)^k) * e^y
+
+    for y in (-inf, +inf), k > 0, lam > 0.
+
+    Since Y = ln(lam) + (1/k)*ln(W) where W ~ Exp(1), the moments are:
+
+        E[Y]   = ln(lam) + psi(1)/k
+        Var[Y] = psi_1(1) / k^2
+
+    Skewness and excess kurtosis are k-independent constants (the 1/k scaling
+    cancels in the standardised moments) given by psi_2(1)/psi_1(1)^(3/2) and
+    psi_3(1)/psi_1(1)^2 respectively.
+
+    The differential entropy is lam-independent:
+
+        H(Y) = 1 - psi(1) - ln(k)
+    """
+
+    def _shape_info(self):
+        return [
+            _ShapeInfo("k", False, (0, np.inf), (False, False)),
+            _ShapeInfo("lam", False, (0, np.inf), (False, False)),
+        ]
+
+    def _argcheck(self, k, lam):
+        return (k > 0) & (lam > 0)
+
+    def _pdf(self, y, k, lam):
+        return np.exp(self._logpdf(y, k, lam))
+
+    def _logpdf(self, y, k, lam):
+        # ln f = ln(k) + k*(y - ln(lam)) - (e^y/lam)^k
+        return np.log(k) + k * (y - np.log(lam)) - (np.exp(y) / lam) ** k
+
+    def _cdf(self, y, k, lam):
+        return 1.0 - np.exp(-((np.exp(y) / lam) ** k))
+
+    def _sf(self, y, k, lam):
+        return np.exp(-((np.exp(y) / lam) ** k))
+
+    def _logcdf(self, y, k, lam):
+        return np.log1p(-np.exp(-((np.exp(y) / lam) ** k)))
+
+    def _logsf(self, y, k, lam):
+        return -((np.exp(y) / lam) ** k)
+
+    def _ppf(self, q, k, lam):
+        # q = 1 - exp(-(e^y/lam)^k)  =>  y = ln(lam) + ln(-log1p(-q)) / k
+        return np.log(lam) + np.log(-np.log1p(-q)) / k
+
+    def _isf(self, q, k, lam):
+        # q = exp(-(e^y/lam)^k)  =>  y = ln(lam) + ln(-ln(q)) / k
+        return np.log(lam) + np.log(-np.log(q)) / k
+
+    def _stats(self, k, lam):
+        # Y = ln(lam) + (1/k)*ln(W), W ~ Exp(1) = Gamma(1, 1)
+        mu = np.log(lam) + sc.digamma(1) / k
+        mu2 = sc.polygamma(1, 1) / k ** 2
+        g1 = sc.polygamma(2, 1) / sc.polygamma(1, 1) ** 1.5
+        g2 = sc.polygamma(3, 1) / sc.polygamma(1, 1) ** 2
+        return mu, mu2, g1, g2
+
+    def _entropy(self, k, lam):
+        # H(Y) = 1 - psi(1) - ln(k)  (lam-independent: pure location shift)
+        return 1.0 - sc.digamma(1) - np.log(k)
+
+    def _rvs(self, k, lam, size=None, random_state=None):
+        # X = lam * W^(1/k), W ~ Exp(1)  =>  Y = ln(lam) + ln(W)/k
+        return np.log(lam) + np.log(random_state.exponential(size=size)) / k
+
+
+logweibull = logweibull_gen(name="logweibull", shapes="k, lam")
+
+
+class logricegamma_gen(rv_continuous):
+    """Log-RiceGamma continuous random variable.
+
+    Y = ln(X) where X has the Rice-Gamma PDF:
+
+        f(x; alpha, beta, K) =
+            4*x*(1+K)*exp(-K) / (Gamma(alpha)*beta^alpha)
+            * sum_{n=0}^inf  [K*(1+K)]^n / (n!)^2
+                             * x^{2n} * [beta*(1+K)*x^2]^{(alpha-1-n)/2}
+                             * K_{alpha-1-n}(2*x*sqrt((1+K)/beta))
+
+    for x > 0, giving Y = ln(X) with support on all of R.
+
+    Parameters
+    ----------
+    alpha : float > 0
+        Shape of the Gamma texture distribution.
+    beta  : float > 0
+        Scale of the Gamma texture (E[Omega] = alpha*beta).
+    K     : float >= 0
+        Rice K-factor (specular-to-diffuse power ratio). K=0 recovers
+        the Rayleigh-Gamma (K-distribution) log-envelope.
+
+    The compound representation is: Omega ~ Gamma(alpha, beta), then
+    X|Omega ~ Rice(nu, sigma) with sigma^2 = Omega/(2*(1+K)) and
+    nu = sqrt(K*Omega/(1+K)).
+    """
+    def _shape_info(self):
+        return [
+            _ShapeInfo("alpha", False, (0, np.inf), (False, False)),
+            _ShapeInfo("beta",  False, (0, np.inf), (False, False)),
+            _ShapeInfo("K",     False, (0, np.inf), (True,  False)),
+        ]
+
+    def _argcheck(self, alpha, beta, K):
+        return (alpha > 0) & (beta > 0) & (K >= 0)
+
+    @staticmethod
+    def _log_kve(v, z):
+        """log(kve(v, z)) = log(K_v(z)) + z, numerically stable."""
+        v = np.asarray(v, dtype=float)
+        z = np.asarray(z, dtype=float)
+        abs_v = np.abs(v)
+        with np.errstate(divide='ignore', invalid='ignore', over='ignore'):
+            kve_val = sc.kve(v, z)
+        z_safe = np.where(z > 0, z, 1.0)
+        mu_v = 4.0 * v ** 2
+        log1p_arg = np.maximum(
+            (mu_v - 1.0) / (8.0 * z_safe)
+            + (mu_v - 1.0) * (mu_v - 9.0) / (128.0 * z_safe ** 2),
+            -1.0 + 1e-15,
+        )
+        log_asymp_largez = (
+            0.5 * (np.log(np.pi) - np.log(2.0) - np.log(z_safe))
+            + np.log1p(log1p_arg)
+        )
+        # log(kve(v,z)) ≈ gammaln(|v|) + |v|*log(2/z) - log(2) + z  for |v| >> z
+        log_asymp_largev = (
+            sc.gammaln(np.maximum(abs_v, 1e-300))
+            + abs_v * np.log(2.0 / z_safe)
+            - np.log(2.0)
+            + z
+        )
+        with np.errstate(divide='ignore', invalid='ignore'):
+            kve_bad = ~np.isfinite(kve_val) | (kve_val <= 0)
+            use_largev = (abs_v > z_safe + 2.0) & kve_bad
+            log_asymp = np.where(use_largev, log_asymp_largev, log_asymp_largez)
+            return np.where(kve_bad, log_asymp, np.log(kve_val))
+
+    def _pdf(self, y, alpha, beta, K):
+        return np.exp(self._logpdf(y, alpha, beta, K))
+
+    #: Number of terms kept in the truncated series for _logpdf.
+    #: Increase for large K-factors (rule of thumb: N_SERIES > 3*K + 30).
+    N_SERIES: int = 90
+
+    def _logpdf(self, y, alpha, beta, K):
+        y = np.asarray(y, dtype=float)
+        x = np.exp(y)
+        z = 2.0 * x * np.sqrt((1.0 + K) / beta)
+
+        # log-prefactor: log(4 x^2 (1+K) e^{-K} / (Γ(α) β^α)), absorbs exp(-z)
+        # so each series term uses kve-scaled Bessel values
+        log_pre = (
+            np.log(4.0) + 2.0 * y + np.log(1.0 + K) - K
+            - sc.gammaln(alpha) - alpha * np.log(beta)
+            - z
+        )
+        log_b1Kx2 = np.log(beta) + np.log(1.0 + K) + 2.0 * y  # log[beta*(1+K)*x^2]
+
+        log1pK = np.log(1.0 + K)
+        logK_safe = np.log(np.where(K > 0, K, 1.0))
+
+        log_terms = []
+        for n in range(self.N_SERIES + 1):
+            # log(kve(alpha-1-n, z)) = log(K_{alpha-1-n}(z)) + z
+            log_kve_n = logricegamma_gen._log_kve(alpha - 1.0 - n, z)
+
+            # K^n: for K=0 only the n=0 term survives (0^0 = 1)
+            n_logK = 0.0 if n == 0 else np.where(K > 0, n * logK_safe, -np.inf)
+
+            log_Tn = (
+                n_logK
+                + n * log1pK
+                - 2.0 * float(sc.gammaln(n + 1))
+                + 2.0 * n * y                          # x^{2n} factor
+                + (alpha - 1.0 - n) / 2.0 * log_b1Kx2
+                + log_kve_n
+            )
+            log_terms.append(log_Tn)
+
+        log_arr = np.stack(log_terms, axis=0)           # shape (N_MAX+1, *y.shape)
+        max_lt = np.max(log_arr, axis=0)                # shape (*y.shape)
+        with np.errstate(invalid='ignore'):
+            shifted = log_arr - max_lt[np.newaxis, ...]
+        log_sum = max_lt + np.log(np.sum(np.exp(shifted), axis=0))
+        return log_pre + log_sum
+
+    def _fitstart(self, data, args=None):
+        # loc near the data mean; alpha/beta in (0.5, 1) for typical heavy-tail
+        # radar clutter; K=1 moderate Rice factor; scale near data std.
+        mean_d = float(np.mean(data))
+        std_d  = float(np.std(data))
+        return (0.75, 0.75, 3.0, mean_d, max(std_d * 0.5, 0.1))
+
+    def _rvs(self, alpha, beta, K, size=None, random_state=None):
+        # Compound sampler: Omega ~ Gamma(alpha, beta), X|Omega ~ Rice(nu, sigma)
+        Omega = random_state.gamma(alpha, beta, size=size)
+        sigma = np.sqrt(Omega / (2.0 * (1.0 + K)))
+        nu = np.sqrt(K * Omega / (1.0 + K))
+        z1 = random_state.normal(nu, sigma, size=size)
+        z2 = random_state.normal(0.0, sigma, size=size)
+        return np.log(np.hypot(z1, z2))
+
+    def _cdf(self, y, alpha, beta, K):
+        # Compound representation:
+        #   P(Y <= y) = E_Omega[ P(X <= e^y | Omega) ]
+        # Given Omega, sigma^2 = Omega/(2(1+K)), nu^2 = K*Omega/(1+K):
+        #   P(X <= x | Omega) = ncx2.cdf(x^2/sigma^2, 2, nu^2/sigma^2)
+        #                     = ncx2.cdf(2(1+K)e^{2y}/Omega, 2, 2K)
+        # Non-centrality 2K is Omega-independent.  Integrate over Omega ~ Gamma(alpha, beta)
+        # by substituting s = Omega/beta  (so s ~ Gamma(alpha, 1)) and applying
+        # generalized Gauss-Laguerre quadrature of order alpha-1.
+        from scipy.special import roots_genlaguerre
+        from scipy.special import gamma as sp_gamma
+
+        y = np.asarray(y, dtype=float)
+        # Parameters are broadcast to y's shape by scipy; take the unique scalar.
+        alpha_s = float(np.ravel(alpha)[0])
+        beta_s  = float(np.ravel(beta)[0])
+        K_s     = float(np.ravel(K)[0])
+
+        _N_PTS = 50
+        nodes, weights = roots_genlaguerre(_N_PTS, alpha_s - 1.0)
+
+        # ncx2_arg shape: (*y.shape, N_PTS)
+        ncx2_arg = (
+            2.0 * (1.0 + K_s) * np.exp(2.0 * y)[..., np.newaxis]
+            / (beta_s * nodes)
+        )
+        cdf_vals = ncx2.cdf(ncx2_arg, 2.0, 2.0 * K_s)
+        return np.dot(cdf_vals, weights) / sp_gamma(alpha_s)
+
+
+logricegamma = logricegamma_gen(name='logricegamma', shapes='alpha, beta, K')
+
+
+class ricegamma_gen(rv_continuous):
+    """RiceGamma continuous random variable (linear-domain envelope).
+
+    The probability density function is:
+
+        f(x; alpha, beta, K) =
+            4*x*(1+K)*exp(-K) / (Gamma(alpha)*beta^alpha)
+            * sum_{n=0}^inf  [K*(1+K)]^n / (n!)^2
+                             * x^{2n} * [beta*(1+K)*x^2]^{(alpha-1-n)/2}
+                             * K_{alpha-1-n}(2*x*sqrt((1+K)/beta))
+
+    for x > 0, alpha > 0, beta > 0, K >= 0.
+
+    This is the linear-domain counterpart of logricegamma: if X ~ ricegamma
+    then ln(X) ~ logricegamma (same alpha, beta, K, loc=0, scale=1).
+
+    The compound representation is: Omega ~ Gamma(alpha, beta), then
+    X|Omega ~ Rice(nu, sigma) with sigma^2 = Omega/(2*(1+K)) and
+    nu = sqrt(K*Omega/(1+K)).  E[X^2] = alpha*beta.
+    """
+
+    #: Number of series terms. Increase for large K (rule: N_SERIES > 3*K + 30).
+    N_SERIES: int = 90
+
+    def _shape_info(self):
+        return [
+            _ShapeInfo("alpha", False, (0, np.inf), (False, False)),
+            _ShapeInfo("beta",  False, (0, np.inf), (False, False)),
+            _ShapeInfo("K",     False, (0, np.inf), (True,  False)),
+        ]
+
+    def _argcheck(self, alpha, beta, K):
+        return (alpha > 0) & (beta > 0) & (K >= 0)
+
+    @staticmethod
+    def _log_kve(v, z):
+        """log(kve(v, z)) = log(K_v(z)) + z, numerically stable."""
+        v = np.asarray(v, dtype=float)
+        z = np.asarray(z, dtype=float)
+        abs_v = np.abs(v)
+        with np.errstate(divide='ignore', invalid='ignore', over='ignore'):
+            kve_val = sc.kve(v, z)
+        z_safe = np.where(z > 0, z, 1.0)
+        mu_v = 4.0 * v ** 2
+        log1p_arg = np.maximum(
+            (mu_v - 1.0) / (8.0 * z_safe)
+            + (mu_v - 1.0) * (mu_v - 9.0) / (128.0 * z_safe ** 2),
+            -1.0 + 1e-15,
+        )
+        log_asymp_largez = (
+            0.5 * (np.log(np.pi) - np.log(2.0) - np.log(z_safe))
+            + np.log1p(log1p_arg)
+        )
+        log_asymp_largev = (
+            sc.gammaln(np.maximum(abs_v, 1e-300))
+            + abs_v * np.log(2.0 / z_safe)
+            - np.log(2.0)
+            + z
+        )
+        with np.errstate(divide='ignore', invalid='ignore'):
+            kve_bad = ~np.isfinite(kve_val) | (kve_val <= 0)
+            use_largev = (abs_v > z_safe + 2.0) & kve_bad
+            log_asymp = np.where(use_largev, log_asymp_largev, log_asymp_largez)
+            return np.where(kve_bad, log_asymp, np.log(kve_val))
+
+    def _pdf(self, x, alpha, beta, K):
+        return np.exp(self._logpdf(x, alpha, beta, K))
+
+    def _logpdf(self, x, alpha, beta, K):
+        x = np.asarray(x, dtype=float)
+        z = 2.0 * x * np.sqrt((1.0 + K) / beta)
+
+        # log-prefactor: log(4 x (1+K) e^{-K} / (Γ(α) β^α)), absorbs exp(-z)
+        log_pre = (
+            np.log(4.0) + np.log(x) + np.log(1.0 + K) - K
+            - sc.gammaln(alpha) - alpha * np.log(beta)
+            - z
+        )
+        log_b1Kx2 = np.log(beta) + np.log(1.0 + K) + 2.0 * np.log(x)
+
+        log1pK    = np.log(1.0 + K)
+        logK_safe = np.log(np.where(K > 0, K, 1.0))
+
+        log_terms = []
+        for n in range(self.N_SERIES + 1):
+            log_kve_n = ricegamma_gen._log_kve(alpha - 1.0 - n, z)
+
+            n_logK = 0.0 if n == 0 else np.where(K > 0, n * logK_safe, -np.inf)
+
+            log_Tn = (
+                n_logK
+                + n * log1pK
+                - 2.0 * float(sc.gammaln(n + 1))
+                + 2.0 * n * np.log(x)               # x^{2n} factor
+                + (alpha - 1.0 - n) / 2.0 * log_b1Kx2
+                + log_kve_n
+            )
+            log_terms.append(log_Tn)
+
+        log_arr = np.stack(log_terms, axis=0)
+        max_lt  = np.max(log_arr, axis=0)
+        with np.errstate(invalid='ignore'):
+            shifted = log_arr - max_lt[np.newaxis, ...]
+        log_sum = max_lt + np.log(np.sum(np.exp(shifted), axis=0))
+        return log_pre + log_sum
+
+    def _cdf(self, x, alpha, beta, K):
+        # P(X <= x | Omega) = ncx2.cdf(2*(1+K)*x^2/Omega, 2, 2K)
+        # Integrate out Omega ~ Gamma(alpha, beta) via generalised Gauss-Laguerre.
+        from scipy.special import roots_genlaguerre
+        from scipy.special import gamma as sp_gamma
+
+        x       = np.asarray(x, dtype=float)
+        alpha_s = float(np.ravel(alpha)[0])
+        beta_s  = float(np.ravel(beta)[0])
+        K_s     = float(np.ravel(K)[0])
+
+        nodes, weights = roots_genlaguerre(50, alpha_s - 1.0)
+
+        ncx2_arg = (
+            2.0 * (1.0 + K_s) * (x[..., np.newaxis] ** 2)
+            / (beta_s * nodes)
+        )
+        cdf_vals = ncx2.cdf(ncx2_arg, 2.0, 2.0 * K_s)
+        return np.dot(cdf_vals, weights) / sp_gamma(alpha_s)
+
+    def _rvs(self, alpha, beta, K, size=None, random_state=None):
+        # Compound sampler: Omega ~ Gamma(alpha, beta), X|Omega ~ Rice(nu, sigma)
+        Omega = random_state.gamma(alpha, beta, size=size)
+        sigma = np.sqrt(Omega / (2.0 * (1.0 + K)))
+        nu    = np.sqrt(K * Omega / (1.0 + K))
+        z1    = random_state.normal(nu,  sigma, size=size)
+        z2    = random_state.normal(0.0, sigma, size=size)
+        return np.hypot(z1, z2)
+
+    def _fitstart(self, data, args=None):
+        # Shapes at scipy's default (1.0); loc = data mean; scale = data std.
+        if args is None:
+            args = (1.0,) * self.numargs
+        return args + (float(np.mean(data)), float(np.std(data)))
+
+
+ricegamma = ricegamma_gen(a=0.0, name='ricegamma', shapes='alpha, beta, K')