diff --git a/docs/examples/gallery/chisquared.md b/docs/examples/gallery/chisquared.md
index 567f89ca..406e5753 100644
--- a/docs/examples/gallery/chisquared.md
+++ b/docs/examples/gallery/chisquared.md
@@ -54,7 +54,7 @@ for nu in nus:
 
 ```{eval-rst}
 ========  ==========================================
-Support   :math:`x \in (0, \infty)`
+Support   :math:`x \in [0, \infty)`
 Mean      :math:`\nu`
 Variance  :math:`2\nu`
 ========  ==========================================
diff --git a/docs/examples/gallery/exponential.md b/docs/examples/gallery/exponential.md
index 8c2302aa..01046341 100644
--- a/docs/examples/gallery/exponential.md
+++ b/docs/examples/gallery/exponential.md
@@ -91,7 +91,7 @@ for beta in betas:
 
 ```{eval-rst}
 ========  ==========================================
-Support   :math:`x \in (0, \infty)`
+Support   :math:`x \in [0, \infty)`
 Mean      :math:`\frac{1}{\lambda}`
 Variance  :math:`\frac{1}{\lambda^2}`
 ========  ==========================================
diff --git a/preliz/distributions/beta.py b/preliz/distributions/beta.py
index 65b24a58..5db3d39c 100644
--- a/preliz/distributions/beta.py
+++ b/preliz/distributions/beta.py
@@ -252,7 +252,7 @@ def nb_entropy(alpha, beta):
 
 @nb.vectorize(nopython=True, cache=True)
 def nb_logpdf(x, alpha, beta):
-    if x < 0 or x > 1:
+    if x <= 0 or x >= 1:
         return -np.inf
     else:
         beta_ = gammaln(alpha) + gammaln(beta) - gammaln(alpha + beta)
diff --git a/preliz/distributions/gamma.py b/preliz/distributions/gamma.py
index 8de9c823..adb2451b 100644
--- a/preliz/distributions/gamma.py
+++ b/preliz/distributions/gamma.py
@@ -191,7 +191,7 @@ def nb_ppf(q, alpha, beta, lower, upper):
 
 @nb.vectorize(nopython=True, cache=True)
 def nb_logpdf(x, alpha, beta):
-    if x < 0:
+    if x <= 0:
         return -np.inf
     else:
         x = x / (1 / beta)
diff --git a/preliz/distributions/hurdle.py b/preliz/distributions/hurdle.py
index 030166fb..0a9af722 100644
--- a/preliz/distributions/hurdle.py
+++ b/preliz/distributions/hurdle.py
@@ -47,13 +47,12 @@ class Hurdle(DistributionTransformer):
         Expected proportion of the base distribution (0 < psi < 1)
     """
 
-    def __init__(self, dist, psi, **kwargs):
+    def __init__(self, dist, psi=None, **kwargs):
         self.dist = dist
-        self.psi = psi
         super().__init__()
-        self._parametrization(**kwargs)
+        self._parametrization(psi, **kwargs)
 
-    def _parametrization(self, **kwargs):
+    def _parametrization(self, psi=None, **kwargs):
         dist_params = []
         if not kwargs:
             if hasattr(self.dist, "params"):
@@ -65,6 +64,7 @@ def _parametrization(self, **kwargs):
             dist_params.append(value)
             setattr(self, key, value)
 
+        self.psi = psi
         self.params = (*dist_params, self.psi)
         self.param_names = (*self.dist.param_names, "psi")
         if all_not_none(*dist_params):
diff --git a/preliz/distributions/kumaraswamy.py b/preliz/distributions/kumaraswamy.py
index 8cb20355..4faafa2e 100644
--- a/preliz/distributions/kumaraswamy.py
+++ b/preliz/distributions/kumaraswamy.py
@@ -173,7 +173,7 @@ def nb_entropy(a, b):
 
 @nb.vectorize(nopython=True, cache=True)
 def nb_logpdf(x, a, b):
-    if x < 0 or x > 1:
+    if x <= 0 or x >= 1:
         return -np.inf
     else:
         return np.log(a * b) + xlogy((a - 1), x) + xlog1py((b - 1), -(x**a))
diff --git a/preliz/tests/test_scipy.py b/preliz/tests/test_scipy.py
index 208f4501..b136a3e9 100644
--- a/preliz/tests/test_scipy.py
+++ b/preliz/tests/test_scipy.py
@@ -87,7 +87,12 @@
             {"loc": 0, "scale": 2},
         ),  # not in scipy
         (InverseGamma, stats.invgamma, {"alpha": 5, "beta": 2}, {"a": 5, "scale": 2}),
-        (Kumaraswamy, stats.beta, {"a": 1, "b": 5}, {"a": 1, "b": 5}),  # not in scipy
+        (
+            Kumaraswamy,
+            stats.beta,
+            {"a": 1.00000001, "b": 5},
+            {"a": 1.00000001, "b": 5},
+        ),  # not in scipy
         (Laplace, stats.laplace, {"mu": 2.5, "b": 4}, {"loc": 2.5, "scale": 4}),
         (LogLogistic, stats.fisk, {"alpha": 1, "beta": 8}, {"c": 8}),
         (Logistic, stats.logistic, {"mu": 2.5, "s": 4}, {"loc": 2.5, "scale": 4}),