ADD:

ruff for code formatting

BIC statistic AND BIC test implemented

test_distributions.py for test new created dists with pytest

REFACTOR:
k_gen pdf changed from 2 params to generalized

etc/tools/distributions.py

@@ -1,43 +1,51 @@
 from scipy.stats import rv_continuous
-from scipy.special import gamma, kv, gammaln
+from scipy.special import kv, gammaln
 from scipy.stats._distn_infrastructure import _ShapeInfo
 import numpy as np
-import pandas as pd
 
 
 class k_gen(rv_continuous):
-    """K distribution for radar clutter modeling.
+    """Generalized K distribution for radar clutter modeling.
 
     The probability density function is::
 
-        f(x; nu, b) = 2/Gamma(nu) * b^((nu+1)/2) * x^((nu-1)/2) * K_{nu-1}(2*sqrt(b*x))
+        f(x; mu, alpha, beta) = 2 / (Gamma(alpha) * Gamma(beta))
+                                * (alpha*beta/mu)^((alpha+beta)/2)
+                                * x^((alpha+beta)/2 - 1)
+                                * K_{alpha-beta}(2*sqrt(alpha*beta*x/mu))
 
-    for x >= 0, where K_{nu-1} is the modified Bessel function of the second
-    kind of order nu-1, nu > 0 is the shape parameter and b > 0 is the rate
-    parameter.
+    for x > 0, where K_{alpha-beta} is the modified Bessel function of the
+    second kind of order alpha-beta, mu > 0 is the mean, and alpha > 0,
+    beta > 0 are shape parameters.
+
+    The standard (2-parameter) K distribution is the special case beta=1,
+    with nu=alpha and b=alpha/mu.
     """
 
     def _shape_info(self):
-        return [_ShapeInfo("nu", domain=(0, np.inf), inclusive=(False, True)),
-                _ShapeInfo("b", domain=(0, np.inf), inclusive=(False, True))]
+        return [
+            _ShapeInfo("mu", domain=(0, np.inf), inclusive=(False, True)),
+            _ShapeInfo("alpha", domain=(0, np.inf), inclusive=(True, True)),
+            _ShapeInfo("beta", domain=(0, np.inf), inclusive=(True, True)),
+        ]
 
+    def _argcheck(self, mu, alpha, beta):
+        return (mu > 0) & (alpha > 0) & (beta > 0)
 
-    def _argcheck(self, nu, b):
-        return (nu > 0) & (b > 0)
+    def _pdf(self, x, mu, alpha, beta):
+        return np.exp(self._logpdf(x, mu, alpha, beta))
 
-    def _pdf(self, x, nu, b):
-        # k.pdf(x, nu, b) = 2/Gamma(nu) * b^((nu+1)/2) * x^((nu-1)/2) * K_{nu-1}(2*sqrt(b*x))
-        return np.exp(self._logpdf(x, nu, b))
-
-    def _logpdf(self, x, nu, b):
+    def _logpdf(self, x, mu, alpha, beta):
+        z = 2.0 * np.sqrt(alpha * beta * x / mu)
         return (
             np.log(2.0)
-            - gammaln(nu)
-            + (nu + 1) / 2.0 * np.log(b)
-            + (nu - 1) / 2.0 * np.log(x)
-            + np.log(kv(nu - 1, 2.0 * np.sqrt(b * x)))
+            - gammaln(alpha)
+            - gammaln(beta)
+            + (alpha + beta) / 2.0 * np.log(alpha * beta / mu)
+            + ((alpha + beta) / 2.0 - 1.0) * np.log(x)
+            + np.log(kv(alpha - beta, z))
         )
 
 
-k_dist = k_gen(a=0.0, name="k_distribution", shapes="nu, b")
+k_dist = k_gen(a=0.0, name="k_distribution", shapes="mu, alpha, beta")