ADD:

`generate_data.py` for processing and fitting statistical distributions to data.

'distributions.py' to create new dists to fit

'analysis_data.ipynb" notebook for data analysis

etc/tools/distributions.py

@@ -0,0 +1,43 @@
+from scipy.stats import rv_continuous
+from scipy.special import gamma, 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.
+
+    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))
+
+    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.
+    """
+
+    def _shape_info(self):
+        return [_ShapeInfo("nu", domain=(0, np.inf), inclusive=(False, True)),
+                _ShapeInfo("b", domain=(0, np.inf), inclusive=(False, True))]
+
+
+    def _argcheck(self, nu, b):
+        return (nu > 0) & (b > 0)
+
+    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):
+        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)))
+        )
+
+
+k_dist = k_gen(a=0.0, name="k_distribution", shapes="nu, b")
+