Normalize gaussian basis (#1912)

* Normalize gaussian basis

* Adapt test to normalization

Author: PabloRoque

pymc_marketing/mmm/events.py

@@ -261,7 +261,9 @@ class GaussianBasis(Basis):
 
     def function(self, x: pt.TensorLike, sigma: pt.TensorLike) -> TensorVariable:
         """Gaussian bump function."""
-        return pm.math.exp(-0.5 * (x / sigma) ** 2)
+        rv = pm.Normal.dist(mu=0.0, sigma=sigma)
+        out = pm.math.exp(pm.logp(rv, x))
+        return out
 
     default_priors = {
         "sigma": Prior("Gamma", mu=7, sigma=1),

tests/mmm/test_events.py

@@ -171,7 +171,7 @@ def test_gaussian_basis_function():
     sigma = np.array([1.0])
 
     result = gaussian.function(x, sigma).eval()
-    expected = np.exp(-0.5 * (x / sigma) ** 2)
+    expected = 1 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-0.5 * (x / sigma) ** 2)
 
     np.testing.assert_array_almost_equal(result, expected)