diff --git a/numpy/random/generator.pyx b/numpy/random/generator.pyx
index 6fa24b967856..fed978e70a9a 100644
--- a/numpy/random/generator.pyx
+++ b/numpy/random/generator.pyx
@@ -115,9 +115,7 @@ cdef class RandomGenerator:
 
     def __reduce__(self):
         from ._pickle import __generator_ctor
-        return (__generator_ctor,
-                (self.brng.state['brng'],),
-                self.brng.state)
+        return __generator_ctor, (self.brng.state['brng'],), self.brng.state
 
     def random_sample(self, size=None, dtype=np.float64, out=None):
         """
@@ -3323,7 +3321,7 @@ cdef class RandomGenerator:
         nbad : int or array_like of ints
             Number of ways to make a bad selection.  Must be nonnegative.
         nsample : int or array_like of ints
-            Number of items sampled.  Must be at least 1 and at most
+            Number of items sampled.  Must be nonnegative and less than
             ``ngood + nbad``.
         size : int or tuple of ints, optional
             Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
@@ -3415,14 +3413,14 @@ cdef class RandomGenerator:
             return disc(&random_hypergeometric, self._brng, size, self.lock, 0, 3,
                         lngood, 'ngood', CONS_NON_NEGATIVE,
                         lnbad, 'nbad', CONS_NON_NEGATIVE,
-                        lnsample, 'nsample', CONS_GTE_1)
+                        lnsample, 'nsample', CONS_NON_NEGATIVE)
 
         if np.any(np.less(np.add(ongood, onbad), onsample)):
             raise ValueError("ngood + nbad < nsample")
         return discrete_broadcast_iii(&random_hypergeometric, self._brng, size, self.lock,
                                       ongood, 'ngood', CONS_NON_NEGATIVE,
                                       onbad, 'nbad', CONS_NON_NEGATIVE,
-                                      onsample, 'nsample', CONS_GTE_1)
+                                      onsample, 'nsample', CONS_NON_NEGATIVE)
 
     def logseries(self, p, size=None):
         """
diff --git a/numpy/random/legacy/legacy_distributions.pxd b/numpy/random/legacy_distributions.pxd
similarity index 98%
rename from numpy/random/legacy/legacy_distributions.pxd
rename to numpy/random/legacy_distributions.pxd
index bc00994dbacb..08dde3315c34 100644
--- a/numpy/random/legacy/legacy_distributions.pxd
+++ b/numpy/random/legacy_distributions.pxd
@@ -5,7 +5,7 @@ from libc.stdint cimport uint64_t
 import numpy as np
 cimport numpy as np
 
-from ..distributions cimport brng_t
+from .distributions cimport brng_t
 
 cdef extern from "../src/legacy/distributions-boxmuller.h":
 
diff --git a/numpy/random/mtrand.pyx b/numpy/random/mtrand.pyx
index 2d3ea32cba5a..3f73981cd918 100644
--- a/numpy/random/mtrand.pyx
+++ b/numpy/random/mtrand.pyx
@@ -15,7 +15,7 @@ from .bounded_integers cimport *
 from .bounded_integers import _randint_types
 from .common cimport *
 from .distributions cimport *
-from .legacy.legacy_distributions cimport *
+from .legacy_distributions cimport *
 from .mt19937 import MT19937 as _MT19937
 
 np.import_array()
@@ -113,9 +113,7 @@ cdef class RandomState:
     def __reduce__(self):
         state = self.get_state(legacy=False)
         from ._pickle import __randomstate_ctor
-        return (__randomstate_ctor,
-                (state['brng'],),
-                state)
+        return __randomstate_ctor, (state['brng'],), state
 
     cdef _reset_gauss(self):
         self._aug_state.has_gauss = 0
diff --git a/numpy/random/tests/test_generator_mt19937.py b/numpy/random/tests/test_generator_mt19937.py
index d591ca3399e9..ff5dc01504df 100644
--- a/numpy/random/tests/test_generator_mt19937.py
+++ b/numpy/random/tests/test_generator_mt19937.py
@@ -1837,7 +1837,7 @@ def test_hypergeometric(self):
         nsample = [2]
         bad_ngood = [-1]
         bad_nbad = [-2]
-        bad_nsample_one = [0]
+        bad_nsample_one = [-1]
         bad_nsample_two = [4]
         hypergeom = random.hypergeometric
         desired = np.array([1, 1, 1])
@@ -1868,7 +1868,7 @@ def test_hypergeometric(self):
 
         assert_raises(ValueError, hypergeom, -1, 10, 20)
         assert_raises(ValueError, hypergeom, 10, -1, 20)
-        assert_raises(ValueError, hypergeom, 10, 10, 0)
+        assert_raises(ValueError, hypergeom, 10, 10, -1)
         assert_raises(ValueError, hypergeom, 10, 10, 25)
 
     def test_logseries(self):