diff --git a/examples/model.py b/examples/model.py
index aba8d3d..5c32053 100644
--- a/examples/model.py
+++ b/examples/model.py
@@ -19,7 +19,9 @@ def __call__(self, processes: dict, parameters: dict) -> dlx.Result:
 
         bkg1_modifier = dlx.compose(
             dlx.modifier(
-                name="lnN1", parameter=parameters["norm1"], effect=dlx.effect.lnN(0.1)
+                name="lnN1",
+                parameter=parameters["norm1"],
+                effect=dlx.effect.lnN((0.9, 1.1)),
             ),
             dlx.modifier(
                 name="shape1_bkg1",
@@ -37,7 +39,9 @@ def __call__(self, processes: dict, parameters: dict) -> dlx.Result:
 
         bkg2_modifier = dlx.compose(
             dlx.modifier(
-                name="lnN2", parameter=parameters["norm2"], effect=dlx.effect.lnN(0.05)
+                name="lnN2",
+                parameter=parameters["norm2"],
+                effect=dlx.effect.lnN((0.95, 1.05)),
             ),
             dlx.modifier(
                 name="shape1_bkg2",
diff --git a/src/dilax/effect.py b/src/dilax/effect.py
index 076d78f..2095b3a 100644
--- a/src/dilax/effect.py
+++ b/src/dilax/effect.py
@@ -10,6 +10,8 @@
 from dilax.pdf import Flat, Gauss, HashablePDF, Poisson
 from dilax.util import as1darray
 
+ArrayLike = jax.typing.ArrayLike
+
 if TYPE_CHECKING:
     from dilax.parameter import Parameter
 
@@ -51,9 +53,9 @@ def scale_factor(self, parameter: Parameter, sumw: jax.Array) -> jax.Array:
 
 
 class gauss(Effect):
-    width: jax.Array = eqx.field(static=True, converter=as1darray)
+    width: ArrayLike = eqx.field(static=True, converter=as1darray)
 
-    def __init__(self, width: jax.Array) -> None:
+    def __init__(self, width: ArrayLike) -> None:
         self.width = width
 
     @property
@@ -124,21 +126,29 @@ def scale_factor(self, parameter: Parameter, sumw: jax.Array) -> jax.Array:
 
 
 class lnN(Effect):
-    width: jax.Array | tuple[jax.Array, jax.Array] = eqx.field(static=True)
+    width: tuple[ArrayLike, ArrayLike] = eqx.field(static=True)
 
     def __init__(
         self,
-        width: jax.Array | tuple[jax.Array, jax.Array],
+        width: tuple[ArrayLike, ArrayLike],
     ) -> None:
         self.width = width
 
-    def scale(self, parameter: Parameter) -> jax.Array:
-        if isinstance(self.width, tuple):
-            down, up = self.width
-            scale = jnp.where(parameter.value > 0, up, down)
-        else:
-            scale = self.width
-        return scale
+    def interpolate(self, parameter: Parameter) -> jax.Array:
+        # https://github.com/cms-analysis/HiggsAnalysis-CombinedLimit/blob/be488af288361ef101859a398ae618131373cad7/src/ProcessNormalization.cc#L112-L129
+        x = parameter.value
+        lo, hi = self.width
+        hi = jnp.log(hi)
+        lo = jnp.log(lo)
+        lo = -lo
+        avg = 0.5 * (hi + lo)
+        halfdiff = 0.5 * (hi - lo)
+        twox = x + x
+        twox2 = twox * twox
+        alpha = 0.125 * twox * (twox2 * (3 * twox2 - 10.0) + 15.0)
+        return jnp.where(
+            jnp.abs(x) >= 0.5, jnp.where(x >= 0, hi, lo), avg + alpha * halfdiff
+        )
 
     @property
     def constraint(self) -> HashablePDF:
@@ -159,10 +169,10 @@ def scale_factor(self, parameter: Parameter, sumw: jax.Array) -> jax.Array:
 
             .. code-block:: python
 
-                return jnp.exp(parameter.value * self.scale(parameter=parameter))
+                return jnp.exp(parameter.value * self.interpolate(parameter=parameter))
 
         """
-        return jnp.exp(parameter.value * self.scale(parameter=parameter))
+        return jnp.exp(parameter.value * self.interpolate(parameter=parameter))
 
 
 class poisson(Effect):
diff --git a/src/dilax/likelihood.py b/src/dilax/likelihood.py
index f5bf087..b0aca47 100644
--- a/src/dilax/likelihood.py
+++ b/src/dilax/likelihood.py
@@ -47,14 +47,16 @@ def __call__(self, values: dict | Sentinel = _NoValue) -> jax.Array:
             values = self.model.parameter_values
         model = self.model.update(values=values)
         res = model.evaluate()
-        nll = self.logpdf(self.observation, res.expectation()) - self.logpdf(
-            self.observation, self.observation
+        nll = jnp.sum(
+            self.logpdf(self.observation, res.expectation())
+            - self.logpdf(self.observation, self.observation),
+            axis=-1,
         )
         # add constraints
         constraints = jax.tree_util.tree_leaves(model.parameter_constraints())
         nll += sum(constraints)
         nll += model.nll_boundary_penalty()
-        return -jnp.sum(nll, axis=-1)
+        return -jnp.sum(nll)
 
 
 class Hessian(BaseModule):
diff --git a/src/dilax/util.py b/src/dilax/util.py
index aa4de84..cc7f667 100644
--- a/src/dilax/util.py
+++ b/src/dilax/util.py
@@ -8,6 +8,8 @@
 import jax
 import jax.numpy as jnp
 
+ArrayLike = jax.typing.ArrayLike
+
 __all__ = [
     "HistDB",
     "FrozenDB",
@@ -256,7 +258,7 @@ class HistDB(FrozenDB):
     )
 
 
-def as1darray(x: float | jax.Array) -> jax.Array:
+def as1darray(x: ArrayLike) -> jax.Array:
     """
     Converts `x` to a 1d array.
 
diff --git a/tests/test_parameter.py b/tests/test_parameter.py
index 276e874..57df052 100644
--- a/tests/test_parameter.py
+++ b/tests/test_parameter.py
@@ -42,7 +42,7 @@ def test_gauss():
 
 def test_lnN():
     p = dlx.Parameter(value=jnp.array(0.0))
-    ln = dlx.effect.lnN(width=jnp.array(0.1))
+    ln = dlx.effect.lnN(width=(0.9, 1.1))
 
     assert ln.constraint == Gauss(mean=0.0, width=1.0)
     assert ln.scale_factor(p, jnp.array(1.0)) == pytest.approx(1.0)
@@ -80,7 +80,7 @@ def test_modifier():
 
     # lnN effect
     m_lnN = dlx.modifier(
-        name="norm", parameter=norm, effect=dlx.effect.lnN(jnp.array(0.1))
+        name="norm", parameter=norm, effect=dlx.effect.lnN(width=(0.9, 1.1))
     )
     assert m_lnN(jnp.array(10)) == pytest.approx(10)