Adding Interpolated moment (#5222)

* Added Interpolated moments and tests


Co-authored-by: Ricardo Vieira <[email protected]>

Author: larryshamalama

pymc/distributions/continuous.py

@@ -3686,6 +3686,15 @@ def dist(cls, x_points, pdf_points, *args, **kwargs):
 
         return super().dist([x_points, pdf_points, cdf_points], **kwargs)
 
+    def get_moment(rv, size, x_points, pdf_points, cdf_points):
+        # cdf_points argument is unused
+        moment = at.sum(at.mul(x_points, pdf_points))
+
+        if not rv_size_is_none(size):
+            moment = at.full(size, moment)
+
+        return moment
+
     def logp(value, x_points, pdf_points, cdf_points):
         """
         Calculate log-probability of Interpolated distribution at specified value.

pymc/tests/test_distributions_moments.py

@@ -33,6 +33,7 @@
     HalfNormal,
     HalfStudentT,
     HyperGeometric,
+    Interpolated,
     InverseGamma,
     Kumaraswamy,
     Laplace,
@@ -800,6 +801,36 @@ def test_categorical_moment(p, size, expected):
     assert_moment_is_expected(model, expected)
 
 
+@pytest.mark.parametrize(
+    "x_points, pdf_points, size, expected",
+    [
+        (np.array([-1, 1]), np.array([0.4, 0.6]), None, 0.2),
+        (
+            np.array([-4, -1, 3, 9, 19]),
+            np.array([0.1, 0.15, 0.2, 0.25, 0.3]),
+            None,
+            1.5458937198067635,
+        ),
+        (
+            np.array([-22, -4, 0, 8, 13]),
+            np.tile(1 / 5, 5),
+            (5, 3),
+            np.full((5, 3), -0.14285714285714296),
+        ),
+        (
+            np.arange(-100, 10),
+            np.arange(1, 111) / 6105,
+            (2, 5, 3),
+            np.full((2, 5, 3), -27.584097859327223),
+        ),
+    ],
+)
+def test_interpolated_moment(x_points, pdf_points, size, expected):
+    with Model() as model:
+        Interpolated("x", x_points=x_points, pdf_points=pdf_points, size=size)
+    assert_moment_is_expected(model, expected)
+
+
 @pytest.mark.parametrize(
     "mu, cov, size, expected",
     [