diff --git a/RELEASE_NOTES.md b/RELEASE_NOTES.md
index a7ae2fcf..5bc7b392 100644
--- a/RELEASE_NOTES.md
+++ b/RELEASE_NOTES.md
@@ -8,6 +8,7 @@
 * Replace the deprecated `friedman_mse` criterion with `squared_error` for the default tree learner and distribution tests (issue #408, PR #409)
 * Support a distinct base learner for each distribution parameter, including scikit-learn nested parameters and feature importances for all-tree configurations (issue #338, PR #411)
 * Fix the `CRPScore` metric of `Normal`, `NormalFixedMean` and `LogNormal`, which was the correct metric multiplied by the scale. It was too large where the predicted scale is above 1 and too small where it is below 1. Fits that use `CRPScore` with these distributions change wherever the predicted scale is not 1 (issue #421)
+* Add `df` to the `params` of `T`, `TFixedDf`, `TFixedDfFixedVar` and the `Cauchy` classes built on them, so that `scipy.stats.t(**dist.params)` rebuilds the predicted distribution. Before, `params` held only `loc` and `scale`
 
 ## Version 0.5.10
 
diff --git a/ngboost/distns/t.py b/ngboost/distns/t.py
index 4657890a..0b704411 100644
--- a/ngboost/distns/t.py
+++ b/ngboost/distns/t.py
@@ -77,7 +77,7 @@ def __getattr__(self, name):
 
     @property
     def params(self):
-        return {"loc": self.loc, "scale": self.scale}
+        return {"loc": self.loc, "scale": self.scale, "df": self.df}
 
 
 class TFixedDfLogScore(LogScore):
@@ -141,7 +141,7 @@ def __getattr__(self, name):
 
     @property
     def params(self):
-        return {"loc": self.loc, "scale": self.scale}
+        return {"loc": self.loc, "scale": self.scale, "df": self.df}
 
 
 class TFixedDfFixedVarLogScore(LogScore):
@@ -199,4 +199,4 @@ def __getattr__(self, name):
 
     @property
     def params(self):
-        return {"loc": self.loc, "scale": self.scale}
+        return {"loc": self.loc, "scale": self.scale, "df": self.df}
diff --git a/notebooks/example_t.ipynb b/notebooks/example_t.ipynb
index 5367108a..b0293899 100644
--- a/notebooks/example_t.ipynb
+++ b/notebooks/example_t.ipynb
@@ -596,7 +596,7 @@
     "ax = axes[1]\n",
     "x = np.linspace(-5, 12, 300)\n",
     "for i in [0, 50, 100]:\n",
-    "    pdf = scipy.stats.t.pdf(x, df=dists.df[i], loc=dists.loc[i], scale=dists.scale[i])\n",
+    "    pdf = scipy.stats.t.pdf(x, **dists[i].params)\n",
     "    ax.plot(x, pdf, label=f\"sample {i}\")\n",
     "    ax.axvline(Y_test[i], color=ax.lines[-1].get_color(), linestyle=\":\", alpha=0.5)\n",
     "ax.set_xlabel(\"y\")\n",
diff --git a/tests/test_distns.py b/tests/test_distns.py
index 3f7fd9c3..9325e9fa 100644
--- a/tests/test_distns.py
+++ b/tests/test_distns.py
@@ -2,6 +2,7 @@
 
 import numpy as np
 import pytest
+import scipy.stats
 from sklearn.datasets import fetch_california_housing, load_breast_cancer
 from sklearn.model_selection import train_test_split
 from sklearn.tree import DecisionTreeRegressor
@@ -25,6 +26,7 @@
     Weibull,
     k_categorical,
 )
+from ngboost.distns.cauchy import CauchyFixedVar
 from ngboost.scores import CRPScore, LogScore, Score
 
 # test all the dist methods and score implementation methods,#
@@ -224,3 +226,34 @@ def test_multivariatenormal(k: int, learner):
     mean = y_dist.mean
     sample = y_dist.rv()
     scipy_list = y_dist.scipy_distribution()
+
+
+@pytest.mark.parametrize(
+    "dist_class, expected_df",
+    [
+        (T, None),
+        (TFixedDf, 3.0),
+        (TFixedDfFixedVar, 3.0),
+        (Cauchy, 1.0),
+        (CauchyFixedVar, 1.0),
+    ],
+)
+def test_t_family_params_match_scipy(dist_class, expected_df):
+    rng = np.random.default_rng(0)
+    n = 20
+    raw_params = rng.normal(size=(dist_class.n_params, n))
+    dist = dist_class(raw_params)
+    params = dist.params
+
+    # df is reported next to loc and scale, and loc is the first raw parameter
+    assert set(params) == {"loc", "scale", "df"}
+    np.testing.assert_allclose(params["loc"], raw_params[0])
+    np.testing.assert_allclose(params["df"], dist.df)
+    if expected_df is not None:
+        np.testing.assert_allclose(params["df"], expected_df)
+
+    # the params are enough to rebuild the same distribution in scipy
+    y = rng.normal(size=n)
+    frozen = scipy.stats.t(**params)
+    np.testing.assert_allclose(frozen.logpdf(y), dist.logpdf(y))
+    np.testing.assert_allclose(frozen.ppf(0.9), dist.ppf(0.9))