diff --git a/Lib/random.py b/Lib/random.py
index 86d562f0b8aaf6..76507cea49fd51 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -536,6 +536,8 @@ def triangular(self, low=0.0, high=1.0, mode=None):
     def normalvariate(self, mu=0.0, sigma=1.0):
         """Normal distribution.
 
+        Conditions on the parameters are sigma > 0.
+
         mu is the mean, and sigma is the standard deviation.
 
         """
@@ -544,6 +546,9 @@ def normalvariate(self, mu=0.0, sigma=1.0):
         # variables using the ratio of uniform deviates", ACM Trans
         # Math Software, 3, (1977), pp257-260.
 
+        if sigma <= 0:
+            raise ValueError("normalvariate: sigma must be > 0.0")
+
         random = self.random
         while True:
             u1 = random()
@@ -640,7 +645,9 @@ def vonmisesvariate(self, mu, kappa):
 
         random = self.random
         if kappa <= 1e-6:
-            return TWOPI * random()
+            if kappa >= 0:
+                return TWOPI * random()
+            raise ValueError("vonmisesvariate: kappa must be >= 0.0")
 
         s = 0.5 / kappa
         r = s + _sqrt(1.0 + s * s)
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 0217ebd132b110..b0bb0eca3d9f28 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -1084,9 +1084,6 @@ def test_constant(self):
                 (g.expovariate, (float('inf'),), 0.0),
                 (g.vonmisesvariate, (3.0, float('inf')), 3.0),
                 (g.gauss, (10.0, 0.0), 10.0),
-                (g.lognormvariate, (0.0, 0.0), 1.0),
-                (g.lognormvariate, (-float('inf'), 0.0), 0.0),
-                (g.normalvariate, (10.0, 0.0), 10.0),
                 (g.binomialvariate, (0, 0.5), 0),
                 (g.binomialvariate, (10, 0.0), 0),
                 (g.binomialvariate, (10, 1.0), 10),
@@ -1152,7 +1149,13 @@ def test_binomialvariate(self):
         # Demonstrate the BTRS works for huge values of n
         self.assertTrue(19_000_000 <= B(100_000_000, 0.2) <= 21_000_000)
         self.assertTrue(89_000_000 <= B(100_000_000, 0.9) <= 91_000_000)
+    def test_log_norm_errors(self):
+        # sigma must be > 0.0
+        self.assertRaises(ValueError, random.lognormvariate, 1, -2)
 
+    def test_von_mises_errors(self):
+        # kappa must be >= 0.0
+        self.assertRaises(ValueError, random.vonmisesvariate, 1, -2)
 
     def test_von_mises_range(self):
         # Issue 17149: von mises variates were not consistently in the