diff --git a/scipy/stats/tests/test_distributions.py b/scipy/stats/tests/test_distributions.py
index 98eec0892b8a..f58123aab047 100755
--- a/scipy/stats/tests/test_distributions.py
+++ b/scipy/stats/tests/test_distributions.py
@@ -1385,7 +1385,8 @@ def test_logpdf_extreme_values(self):
         # with 64 bit floating point.
         assert_equal(logp, [-800, -800])
 
-    @pytest.mark.parametrize("loc_rvs,scale_rvs", [np.random.rand(2)])
+    @pytest.mark.parametrize("loc_rvs,scale_rvs", [(0.4484955, 0.10216821),
+                                                   (0.62918191, 0.74367064)])
     def test_fit(self, loc_rvs, scale_rvs):
         data = stats.logistic.rvs(size=100, loc=loc_rvs, scale=scale_rvs)
 
@@ -2183,7 +2184,7 @@ def setup_method(self):
         np.random.seed(1234)
 
     @pytest.mark.parametrize("rvs_mu,rvs_loc,rvs_scale",
-                             [(2, 0, 1), (np.random.rand(3)*10)])
+                             [(2, 0, 1), (4.635, 4.362, 6.303)])
     def test_fit(self, rvs_mu, rvs_loc, rvs_scale):
         data = stats.invgauss.rvs(size=100, mu=rvs_mu,
                                   loc=rvs_loc, scale=rvs_scale)
@@ -2214,7 +2215,7 @@ def test_fit(self, rvs_mu, rvs_loc, rvs_scale):
         assert shape_mle1 == shape_mle2 == shape_mle3 == 1.04
 
     @pytest.mark.parametrize("rvs_mu,rvs_loc,rvs_scale",
-                             [(2, 0, 1), (np.random.rand(3)*10)])
+                             [(2, 0, 1), (6.311, 3.225, 4.520)])
     def test_fit_MLE_comp_optimizer(self, rvs_mu, rvs_loc, rvs_scale):
         data = stats.invgauss.rvs(size=100, mu=rvs_mu,
                                   loc=rvs_loc, scale=rvs_scale)
@@ -5120,7 +5121,8 @@ def test_logsf(self):
         y = stats.rayleigh.logsf(50)
         assert_allclose(y, -1250)
 
-    @pytest.mark.parametrize("rvs_loc,rvs_scale", [np.random.rand(2)])
+    @pytest.mark.parametrize("rvs_loc,rvs_scale", [(0.85373171, 0.86932204),
+                                                   (0.20558821, 0.61621008)])
     def test_fit(self, rvs_loc, rvs_scale):
         data = stats.rayleigh.rvs(size=250, loc=rvs_loc, scale=rvs_scale)
 
@@ -5145,7 +5147,7 @@ def scale_mle(data, floc):
         assert_equal(scale, scale_mle(data, loc))
 
     @pytest.mark.parametrize("rvs_loc,rvs_scale", [[0.74, 0.01],
-                                                   np.random.rand(2)])
+                                                   [0.08464463, 0.12069025]])
     def test_fit_comparison_super_method(self, rvs_loc, rvs_scale):
         # test that the objective function result of the analytical MLEs is
         # less than or equal to that of the numerically optimized estimate