Add test for cdf, adapt limit of integration to compute cdf.

tests/test_distributions.py

@@ -138,12 +138,21 @@ def test_multivariate_cdf(self):
         """
          Tests the cdf() function of MulvariateDistribution.
          """
-        p = self.mul_var_dist.cdf([2, 2])
+        p = self.mul_var_dist.cdf([2, 2], lower_integration_limit=[0, 0])
         self.assertAlmostEqual(p, 0, delta=0.01)
 
-        p = self.mul_var_dist.cdf([[2, 20], [2, 16]])
+        p = self.mul_var_dist.cdf([[2, 20], [2, 16]], lower_integration_limit=[0, 0])
         np.testing.assert_allclose(p, [0, 1], atol=0.01)
 
+        # Create a bivariate normal distribution, where we know that at the
+        # peak, the CDF must evaluate to 0.25.
+        dist = NormalDistribution(shape=None, loc=ConstantParam(1), scale=ConstantParam(1))
+        dep = (None, None, None)
+        bivariate_dist = MultivariateDistribution([dist, dist], [dep, dep])
+
+        p = bivariate_dist.cdf([1, 1])
+        self.assertAlmostEqual(p, 0.25, delta=0.001)
+
     def test_multivariate_pdf(self):
         """
         Tests the pdf() function of MulvariateDistribution.

viroconcom/distributions.py

@@ -782,7 +782,7 @@ def __init__(self, distributions=None, dependencies=None):
         if not distributions is None:
             self.add_distributions(distributions, dependencies)
 
-    def cdf(self, x):
+    def cdf(self, x, lower_integration_limit=(-np.inf, -np.inf)):
         """
         Joint cumulative distribution function.
 
@@ -792,6 +792,9 @@ def cdf(self, x):
             Points at which to calculate the cdf.
             Array is of shape (d, n) with d being the number of variables and
             n being the number of points.
+        lower_integration_limit : array_like, optional
+            Lower limits for the ingration of the pdf. Must have a length of n.
+            Defaults to (-np.inf, -np.inf).
         Returns
         -------
         p : array_like
@@ -805,14 +808,14 @@ def cdf(self, x):
             p = np.empty(x1.size)
             if x0.size == 1:
                 p, error = scipy.integrate.nquad(self.pdf_2d, [
-                    [0, x0],
-                    [0, x1]
+                    [lower_integration_limit[0], x0],
+                    [lower_integration_limit[1], x1]
                 ])
             else:
                 for i in range(x0.size):
                     p[i], error = scipy.integrate.nquad(self.pdf_2d, [
-                        [0, x0[i]],
-                        [0, x1[i]]
+                        [lower_integration_limit[0], x0[i]],
+                        [lower_integration_limit[1], x1[i]]
                     ])
         else:
             raise NotImplementedError('CDF is currently only implemented for '