Allow logcdf inference in CustomDist

pymc/distributions/distribution.py

@@ -684,9 +684,11 @@ def rv_op(
             def custom_dist_logp(op, values, size, *params, **kwargs):
                 return logp(values[0], *params[: len(dist_params)])
 
-        @_logcdf.register(rv_type)
-        def custom_dist_logcdf(op, value, size, *params, **kwargs):
-            return logcdf(value, *params[: len(dist_params)])
+        if logcdf is not None:
+
+            @_logcdf.register(rv_type)
+            def custom_dist_logcdf(op, value, size, *params, **kwargs):
+                return logcdf(value, *params[: len(dist_params)])
 
         @_moment.register(rv_type)
         def custom_dist_get_moment(op, rv, size, *params):

tests/distributions/test_distribution.py

@@ -404,6 +404,22 @@ def custom_dist(mu, sigma, size):
         ip = m.initial_point()
         np.testing.assert_allclose(m.compile_logp()(ip), ref_m.compile_logp()(ip))
 
+    def test_logcdf_inference(self):
+        def custom_dist(mu, sigma, size):
+            return pt.exp(pm.Normal.dist(mu, sigma, size=size))
+
+        mu = 1
+        sigma = 1.25
+        test_value = 0.9
+
+        custom_lognormal = CustomDist.dist(mu, sigma, dist=custom_dist)
+        ref_lognormal = LogNormal.dist(mu, sigma)
+
+        np.testing.assert_allclose(
+            pm.logcdf(custom_lognormal, test_value).eval(),
+            pm.logcdf(ref_lognormal, test_value).eval(),
+        )
+
     def test_random_multiple_rngs(self):
         def custom_dist(p, sigma, size):
             idx = pm.Bernoulli.dist(p=p)