diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval.pass.cpp
index 9a7af92931dd3e..568bf34f1ea437 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval.pass.cpp
@@ -63,8 +63,8 @@ int main(int, char**)
         double x_kurtosis = (6 * sqr(d.p()) - 6 * d.p() + 1)/x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
     }
     {
         typedef std::bernoulli_distribution D;
@@ -99,8 +99,8 @@ int main(int, char**)
         double x_kurtosis = (6 * sqr(d.p()) - 6 * d.p() + 1)/x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval_param.pass.cpp
index 5584a9d1644896..dfaa9f1c89f991 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval_param.pass.cpp
@@ -65,8 +65,8 @@ int main(int, char**)
         double x_kurtosis = (6 * sqr(p.p()) - 6 * p.p() + 1)/x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
     }
     {
         typedef std::bernoulli_distribution D;
@@ -103,8 +103,8 @@ int main(int, char**)
         double x_kurtosis = (6 * sqr(p.p()) - 6 * p.p() + 1)/x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.PR44847.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.PR44847.pass.cpp
index 572a59b7a1926a..549f3cee4d4a45 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.PR44847.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.PR44847.pass.cpp
@@ -163,7 +163,7 @@ int main(int, char**) {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.06);
 
     return 0;
 }
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.pass.cpp
index dbdd0972411940..d8852cc3bd09ed 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.pass.cpp
@@ -68,7 +68,7 @@ void test1() {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
 }
 
 template <class T>
@@ -109,8 +109,8 @@ void test2() {
     double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
 }
 
 template <class T>
@@ -151,8 +151,8 @@ void test3() {
     double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.03);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.07);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 2.0);
 }
 
 template <class T>
@@ -292,7 +292,7 @@ void test6() {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs(skew - x_skew) < 0.02);
-    assert(std::abs(kurtosis - x_kurtosis) < 0.01);
+    assert(std::abs(kurtosis - x_kurtosis) < 0.03);
 }
 
 template <class T>
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval_param.pass.cpp
index 78d6aedde73a5d..adbcb78d10f4f2 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval_param.pass.cpp
@@ -72,7 +72,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
     }
     {
         typedef std::binomial_distribution<> D;
@@ -113,8 +113,8 @@ int main(int, char**)
         double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
     }
     {
         typedef std::binomial_distribution<> D;
@@ -155,8 +155,8 @@ int main(int, char**)
         double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.04);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.07);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 2.0);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval.pass.cpp
index 440334ed3488ae..0cdb7fa6312caf 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval.pass.cpp
@@ -77,7 +77,7 @@ void test1() {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 template <class T>
@@ -161,7 +161,7 @@ void test3() {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 template <class T>
@@ -203,7 +203,7 @@ void test4() {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 template <class T>
@@ -245,7 +245,7 @@ void test5() {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 template <class T>
@@ -284,8 +284,8 @@ void test6() {
     double x_var = x_mean / d.p();
     double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
     double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p());
-    assert(std::abs((mean - x_mean) / x_mean) < 0.01);
-    assert(std::abs((var - x_var) / x_var) < 0.01);
+    assert(std::abs((mean - x_mean) / x_mean) < 0.02);
+    assert(std::abs((var - x_var) / x_var) < 0.02);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
     assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
 }
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval_param.pass.cpp
index 16cb7fb0a45f98..16a5bd4c7a33e7 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval_param.pass.cpp
@@ -72,7 +72,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::geometric_distribution<> D;
@@ -156,7 +156,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval.pass.cpp
index d0f6fbf0a1203f..be08361fc27e21 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval.pass.cpp
@@ -74,7 +74,7 @@ void test1() {
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 template <class T>
@@ -115,8 +115,8 @@ void test2() {
     double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.1);
 }
 
 template <class T>
@@ -157,8 +157,8 @@ void test3() {
     double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
 }
 
 template <class T>
@@ -243,8 +243,8 @@ void test5() {
     double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.04);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
 }
 
 template <class T>
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval_param.pass.cpp
index 0b03982a737e57..26bc83382f6850 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval_param.pass.cpp
@@ -72,7 +72,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::negative_binomial_distribution<> D;
@@ -113,8 +113,8 @@ int main(int, char**)
         double x_kurtosis = 6. / p.k() + sqr(p.p()) / (p.k() * (1 - p.p()));
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.1);
     }
     {
         typedef std::negative_binomial_distribution<> D;
@@ -155,8 +155,8 @@ int main(int, char**)
         double x_kurtosis = 6. / p.k() + sqr(p.p()) / (p.k() * (1 - p.p()));
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.cauchy/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.cauchy/eval.pass.cpp
index abc0cc531a117e..83e64046f0dcde 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.cauchy/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.cauchy/eval.pass.cpp
@@ -45,7 +45,7 @@ int main(int, char**)
             u.push_back(d(g));
         std::sort(u.begin(), u.end());
         for (int i = 0; i < N; ++i)
-            assert(std::abs(f(u[i], a, b) - double(i)/N) < .001);
+          assert(std::abs(f(u[i], a, b) - double(i) / N) < .0013);
     }
     {
         typedef std::cauchy_distribution<> D;
@@ -60,7 +60,7 @@ int main(int, char**)
             u.push_back(d(g));
         std::sort(u.begin(), u.end());
         for (int i = 0; i < N; ++i)
-            assert(std::abs(f(u[i], a, b) - double(i)/N) < .001);
+          assert(std::abs(f(u[i], a, b) - double(i) / N) < .0013);
     }
     {
         typedef std::cauchy_distribution<> D;
@@ -75,7 +75,7 @@ int main(int, char**)
             u.push_back(d(g));
         std::sort(u.begin(), u.end());
         for (int i = 0; i < N; ++i)
-            assert(std::abs(f(u[i], a, b) - double(i)/N) < .001);
+          assert(std::abs(f(u[i], a, b) - double(i) / N) < .0013);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval.pass.cpp
index 2a8dfd31aa08eb..559034b2a0ec10 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval.pass.cpp
@@ -70,7 +70,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
     }
     {
         typedef std::chi_squared_distribution<> D;
@@ -109,7 +109,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::chi_squared_distribution<> D;
@@ -148,7 +148,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval_param.pass.cpp
index 52864739c9b3cc..74454f29626724 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval_param.pass.cpp
@@ -72,7 +72,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::chi_squared_distribution<> D;
@@ -113,7 +113,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::chi_squared_distribution<> D;
@@ -154,7 +154,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval.pass.cpp
index 9f25cea6540ec0..745103d13d2859 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval.pass.cpp
@@ -70,8 +70,8 @@ test1()
                       3*std::exp(2*sqr(d.s())) - 6;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.05);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.25);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.1);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 1.9);
 }
 
 void
@@ -115,7 +115,7 @@ test2()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
 }
 
 void
@@ -159,7 +159,7 @@ test3()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.02);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.06);
 }
 
 void
@@ -202,8 +202,8 @@ test4()
                       3*std::exp(2*sqr(d.s())) - 6;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.02);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.08);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.4);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.1);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.5);
 }
 
 void
@@ -245,9 +245,9 @@ test5()
     double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) +
                       3*std::exp(2*sqr(d.s())) - 6;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
-    assert(std::abs((var - x_var) / x_var) < 0.04);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.2);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.7);
+    assert(std::abs((var - x_var) / x_var) < 0.05);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.3);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 1.0);
 }
 
 int main(int, char**)
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval_param.pass.cpp
index 9c9eb858e5bfa9..f9ea0bbd201ce1 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval_param.pass.cpp
@@ -72,8 +72,8 @@ test1()
                       3*std::exp(2*sqr(p.s())) - 6;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.05);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.25);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.1);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 1.9);
 }
 
 void
@@ -119,7 +119,7 @@ test2()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
 }
 
 void
@@ -165,7 +165,7 @@ test3()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.02);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.06);
 }
 
 void
@@ -210,8 +210,8 @@ test4()
                       3*std::exp(2*sqr(p.s())) - 6;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.02);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.08);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.4);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.1);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.5);
 }
 
 void
@@ -255,9 +255,9 @@ test5()
     double x_kurtosis = std::exp(4*sqr(p.s())) + 2*std::exp(3*sqr(p.s())) +
                       3*std::exp(2*sqr(p.s())) - 6;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
-    assert(std::abs((var - x_var) / x_var) < 0.04);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.2);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.7);
+    assert(std::abs((var - x_var) / x_var) < 0.05);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.3);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 1.0);
 }
 
 int main(int, char**)
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval.pass.cpp
index a73e06bbf03e96..80ed7bab265022 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval.pass.cpp
@@ -64,7 +64,7 @@ int main(int, char**)
         double x_kurtosis = 6 / (d.n() - 4);
         assert(std::abs(mean - x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs(skew - x_skew) < 0.01);
+        assert(std::abs(skew - x_skew) < 0.05);
         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
     }
     {
@@ -99,7 +99,7 @@ int main(int, char**)
         double x_kurtosis = 6 / (d.n() - 4);
         assert(std::abs(mean - x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs(skew - x_skew) < 0.01);
+        assert(std::abs(skew - x_skew) < 0.05);
         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
     }
     {
@@ -134,8 +134,8 @@ int main(int, char**)
         double x_kurtosis = 6 / (d.n() - 4);
         assert(std::abs(mean - x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs(skew - x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+        assert(std::abs(skew - x_skew) < 0.005);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval_param.pass.cpp
index 01ce61a680af6c..fe3140fb6f555b 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.t/eval_param.pass.cpp
@@ -66,7 +66,7 @@ int main(int, char**)
         double x_kurtosis = 6 / (p.n() - 4);
         assert(std::abs(mean - x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs(skew - x_skew) < 0.01);
+        assert(std::abs(skew - x_skew) < 0.05);
         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
     }
     {
@@ -103,7 +103,7 @@ int main(int, char**)
         double x_kurtosis = 6 / (p.n() - 4);
         assert(std::abs(mean - x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs(skew - x_skew) < 0.01);
+        assert(std::abs(skew - x_skew) < 0.05);
         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
     }
     {
@@ -140,8 +140,8 @@ int main(int, char**)
         double x_kurtosis = 6 / (p.n() - 4);
         assert(std::abs(mean - x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs(skew - x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
+        assert(std::abs(skew - x_skew) < 0.005);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval.pass.cpp
index 8bceb918ecd5d6..aee573e5f2467c 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval.pass.cpp
@@ -70,7 +70,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::exponential_distribution<> D;
@@ -109,7 +109,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::exponential_distribution<> D;
@@ -148,7 +148,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval_param.pass.cpp
index 016ba27587cf7b..dfbedd81e0b976 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.exp/eval_param.pass.cpp
@@ -72,7 +72,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval.pass.cpp
index 9aaf6ce0ab3aed..3cf0feef18ece3 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval.pass.cpp
@@ -68,7 +68,7 @@ test1()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 void
@@ -109,7 +109,7 @@ test2()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 void
@@ -150,7 +150,7 @@ test3()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 void
@@ -191,7 +191,7 @@ test4()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 int main(int, char**)
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval_param.pass.cpp
index cb390c0452ad3e..43a22511589beb 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.extreme/eval_param.pass.cpp
@@ -70,7 +70,7 @@ test1()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 void
@@ -113,7 +113,7 @@ test2()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 void
@@ -156,7 +156,7 @@ test3()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 void
@@ -199,7 +199,7 @@ test4()
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
     assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 }
 
 int main(int, char**)
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval.pass.cpp
index 7af50cdb8b1a98..48cc4df02396f8 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval.pass.cpp
@@ -69,7 +69,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
     }
     {
         typedef std::gamma_distribution<> D;
@@ -108,7 +108,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::gamma_distribution<> D;
@@ -147,7 +147,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval_param.pass.cpp
index a782770153ac5f..c437983c6bd7b1 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.gamma/eval_param.pass.cpp
@@ -71,7 +71,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::gamma_distribution<> D;
@@ -112,7 +112,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
     }
     {
         typedef std::gamma_distribution<> D;
@@ -153,7 +153,7 @@ int main(int, char**)
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval.pass.cpp
index 5feb2e58022916..564f2e99cceacd 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval.pass.cpp
@@ -129,8 +129,8 @@ void tests() {
     double x_kurtosis = 1 / x_var;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.03);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
   }
   {
     typedef std::poisson_distribution<T> D;
@@ -167,9 +167,9 @@ void tests() {
     double x_skew = 1 / std::sqrt(x_var);
     double x_kurtosis = 1 / x_var;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
-    assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
+    assert(std::abs((var - x_var) / x_var) < 0.02);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.09);
   }
   {
     typedef std::poisson_distribution<T> D;
@@ -207,8 +207,8 @@ void tests() {
     double x_kurtosis = 1 / x_var;
     assert(std::abs((mean - x_mean) / x_mean) < 0.01);
     assert(std::abs((var - x_var) / x_var) < 0.01);
-    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+    assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
   }
 }
 
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval_param.pass.cpp
index 8d60be4e656e43..e5cabc08658114 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.poisson/eval_param.pass.cpp
@@ -70,8 +70,8 @@ int main(int, char**)
         double x_kurtosis = 1 / x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.03);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.2);
     }
     {
         typedef std::poisson_distribution<> D;
@@ -110,9 +110,9 @@ int main(int, char**)
         double x_skew = 1 / std::sqrt(x_var);
         double x_kurtosis = 1 / x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
-        assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
+        assert(std::abs((var - x_var) / x_var) < 0.02);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.09);
     }
     {
         typedef std::poisson_distribution<> D;
@@ -152,8 +152,8 @@ int main(int, char**)
         double x_kurtosis = 1 / x_var;
         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
         assert(std::abs((var - x_var) / x_var) < 0.01);
-        assert(std::abs((skew - x_skew) / x_skew) < 0.01);
-        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
+        assert(std::abs((skew - x_skew) / x_skew) < 0.02);
+        assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
     }
 
   return 0;
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.discrete/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.discrete/eval.pass.cpp
index da089b02a96487..9c6365e7e297f3 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.discrete/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.discrete/eval.pass.cpp
@@ -81,7 +81,7 @@ void tests() {
         }
         std::vector<double> prob = d.probabilities();
         for (unsigned i = 0; i < u.size(); ++i)
-            assert(std::abs((double)u[i]/N - prob[i]) / prob[i] < 0.001);
+          assert(std::abs((double)u[i] / N - prob[i]) / prob[i] < 0.0013);
     }
     {
         typedef std::discrete_distribution<T> D;
@@ -158,7 +158,7 @@ void tests() {
         std::vector<double> prob = d.probabilities();
         for (unsigned i = 0; i < u.size(); ++i)
             if (prob[i] != 0)
-                assert(std::abs((double)u[i]/N - prob[i]) / prob[i] < 0.001);
+              assert(std::abs((double)u[i] / N - prob[i]) / prob[i] < 0.0013);
             else
                 assert(u[i] == 0);
     }
@@ -202,7 +202,7 @@ void tests() {
         std::vector<double> prob = d.probabilities();
         for (unsigned i = 0; i < u.size(); ++i)
             if (prob[i] != 0)
-                assert(std::abs((double)u[i]/N - prob[i]) / prob[i] < 0.001);
+              assert(std::abs((double)u[i] / N - prob[i]) / prob[i] < 0.0013);
             else
                 assert(u[i] == 0);
     }
@@ -290,7 +290,7 @@ void tests() {
         std::vector<double> prob = d.probabilities();
         for (unsigned i = 0; i < u.size(); ++i)
             if (prob[i] != 0)
-                assert(std::abs((double)u[i]/N - prob[i]) / prob[i] < 0.001);
+              assert(std::abs((double)u[i] / N - prob[i]) / prob[i] < 0.0013);
             else
                 assert(u[i] == 0);
     }
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.pconst/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.pconst/eval.pass.cpp
index e11b235b7646dc..8ab560b15bb17e 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.pconst/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.pconst/eval.pass.cpp
@@ -529,8 +529,8 @@ test8()
             double x_skew = 0;
             double x_kurtosis = -6./5;
             assert(std::abs((mean - x_mean) / x_mean) < 0.01);
-            assert(std::abs((var - x_var) / x_var) < 0.01);
-            assert(std::abs(skew - x_skew) < 0.01);
+            assert(std::abs((var - x_var) / x_var) < 0.02);
+            assert(std::abs(skew - x_skew) < 0.02);
             assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
         }
     }
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval.pass.cpp
index e551c8c2bb38d2..8aad0b8e4a856d 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval.pass.cpp
@@ -58,7 +58,7 @@ test1()
         u.push_back(v);
     }
     std::sort(u.begin(), u.end());
-    int kp = -1;
+    std::ptrdiff_t kp = -1;
     double a = std::numeric_limits<double>::quiet_NaN();
     double m = std::numeric_limits<double>::quiet_NaN();
     double bk = std::numeric_limits<double>::quiet_NaN();
@@ -76,18 +76,17 @@ test1()
         p[i] /= S;
     for (std::size_t i = 0; i < N; ++i)
     {
-        int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1;
-        if (k != kp)
-        {
-            a = 0;
-            for (int j = 0; j < k; ++j)
-                a += areas[j];
-            m = (p[k+1] - p[k]) / (b[k+1] - b[k]);
-            bk = b[k];
-            c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]);
-            kp = k;
+      std::ptrdiff_t k = std::lower_bound(b, b + Np + 1, u[i]) - b - 1;
+      if (k != kp) {
+        a = 0;
+        for (int j = 0; j < k; ++j)
+          a += areas[j];
+        m  = (p[k + 1] - p[k]) / (b[k + 1] - b[k]);
+        bk = b[k];
+        c  = (b[k + 1] * p[k] - b[k] * p[k + 1]) / (b[k + 1] - b[k]);
+        kp = k;
         }
-        assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001);
+      assert(std::abs(f(u[i], a, m, bk, c) - double(i) / N) < .0013);
     }
 }
 
@@ -110,7 +109,7 @@ test2()
         u.push_back(v);
     }
     std::sort(u.begin(), u.end());
-    int kp = -1;
+    std::ptrdiff_t kp = -1;
     double a = std::numeric_limits<double>::quiet_NaN();
     double m = std::numeric_limits<double>::quiet_NaN();
     double bk = std::numeric_limits<double>::quiet_NaN();
@@ -128,18 +127,17 @@ test2()
         p[i] /= S;
     for (std::size_t i = 0; i < N; ++i)
     {
-        int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1;
-        if (k != kp)
-        {
-            a = 0;
-            for (int j = 0; j < k; ++j)
-                a += areas[j];
-            m = (p[k+1] - p[k]) / (b[k+1] - b[k]);
-            bk = b[k];
-            c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]);
-            kp = k;
+      std::ptrdiff_t k = std::lower_bound(b, b + Np + 1, u[i]) - b - 1;
+      if (k != kp) {
+        a = 0;
+        for (int j = 0; j < k; ++j)
+          a += areas[j];
+        m  = (p[k + 1] - p[k]) / (b[k + 1] - b[k]);
+        bk = b[k];
+        c  = (b[k + 1] * p[k] - b[k] * p[k + 1]) / (b[k + 1] - b[k]);
+        kp = k;
         }
-        assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001);
+      assert(std::abs(f(u[i], a, m, bk, c) - double(i) / N) < .0013);
     }
 }
 
@@ -162,7 +160,7 @@ test3()
         u.push_back(v);
     }
     std::sort(u.begin(), u.end());
-    int kp = -1;
+    std::ptrdiff_t kp = -1;
     double a = std::numeric_limits<double>::quiet_NaN();
     double m = std::numeric_limits<double>::quiet_NaN();
     double bk = std::numeric_limits<double>::quiet_NaN();
@@ -180,18 +178,17 @@ test3()
         p[i] /= S;
     for (std::size_t i = 0; i < N; ++i)
     {
-        int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1;
-        if (k != kp)
-        {
-            a = 0;
-            for (int j = 0; j < k; ++j)
-                a += areas[j];
-            m = (p[k+1] - p[k]) / (b[k+1] - b[k]);
-            bk = b[k];
-            c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]);
-            kp = k;
+      std::ptrdiff_t k = std::lower_bound(b, b + Np + 1, u[i]) - b - 1;
+      if (k != kp) {
+        a = 0;
+        for (int j = 0; j < k; ++j)
+          a += areas[j];
+        m  = (p[k + 1] - p[k]) / (b[k + 1] - b[k]);
+        bk = b[k];
+        c  = (b[k + 1] * p[k] - b[k] * p[k + 1]) / (b[k + 1] - b[k]);
+        kp = k;
         }
-        assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001);
+      assert(std::abs(f(u[i], a, m, bk, c) - double(i) / N) < .0013);
     }
 }
 
@@ -214,7 +211,7 @@ test4()
         u.push_back(v);
     }
     std::sort(u.begin(), u.end());
-    int kp = -1;
+    std::ptrdiff_t kp = -1;
     double a = std::numeric_limits<double>::quiet_NaN();
     double m = std::numeric_limits<double>::quiet_NaN();
     double bk = std::numeric_limits<double>::quiet_NaN();
@@ -232,19 +229,18 @@ test4()
         p[i] /= S;
     for (std::size_t i = 0; i < N; ++i)
     {
-        int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1;
-        if (k != kp)
-        {
-            a = 0;
-            for (int j = 0; j < k; ++j)
-                a += areas[j];
-            assert(k < static_cast<int>(Np));
-            m = (p[k+1] - p[k]) / (b[k+1] - b[k]);
-            bk = b[k];
-            c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]);
-            kp = k;
+      std::ptrdiff_t k = std::lower_bound(b, b + Np + 1, u[i]) - b - 1;
+      if (k != kp) {
+        a = 0;
+        for (int j = 0; j < k; ++j)
+          a += areas[j];
+        assert(k < static_cast<int>(Np));
+        m  = (p[k + 1] - p[k]) / (b[k + 1] - b[k]);
+        bk = b[k];
+        c  = (b[k + 1] * p[k] - b[k] * p[k + 1]) / (b[k + 1] - b[k]);
+        kp = k;
         }
-        assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001);
+      assert(std::abs(f(u[i], a, m, bk, c) - double(i) / N) < .0013);
     }
 }
 
@@ -267,7 +263,7 @@ test5()
         u.push_back(v);
     }
     std::sort(u.begin(), u.end());
-    int kp = -1;
+    std::ptrdiff_t kp = -1;
     double a = std::numeric_limits<double>::quiet_NaN();
     double m = std::numeric_limits<double>::quiet_NaN();
     double bk = std::numeric_limits<double>::quiet_NaN();
@@ -286,19 +282,18 @@ test5()
         p[i] /= S;
     for (std::size_t i = 0; i < N; ++i)
     {
-        int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1;
-        if (k != kp)
-        {
-            a = 0;
-            for (int j = 0; j < k; ++j)
-                a += areas[j];
-            assert(k < static_cast<int>(Np));
-            m = (p[k+1] - p[k]) / (b[k+1] - b[k]);
-            bk = b[k];
-            c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]);
-            kp = k;
+      std::ptrdiff_t k = std::lower_bound(b, b + Np + 1, u[i]) - b - 1;
+      if (k != kp) {
+        a = 0;
+        for (int j = 0; j < k; ++j)
+          a += areas[j];
+        assert(k < static_cast<int>(Np));
+        m  = (p[k + 1] - p[k]) / (b[k + 1] - b[k]);
+        bk = b[k];
+        c  = (b[k + 1] * p[k] - b[k] * p[k + 1]) / (b[k + 1] - b[k]);
+        kp = k;
         }
-        assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001);
+      assert(std::abs(f(u[i], a, m, bk, c) - double(i) / N) < .0013);
     }
 }
 
@@ -321,7 +316,7 @@ test6()
         u.push_back(v);
     }
     std::sort(u.begin(), u.end());
-    int kp = -1;
+    std::ptrdiff_t kp = -1;
     double a = std::numeric_limits<double>::quiet_NaN();
     double m = std::numeric_limits<double>::quiet_NaN();
     double bk = std::numeric_limits<double>::quiet_NaN();
@@ -339,18 +334,17 @@ test6()
         p[i] /= S;
     for (std::size_t i = 0; i < N; ++i)
     {
-        int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1;
-        if (k != kp)
-        {
-            a = 0;
-            for (int j = 0; j < k; ++j)
-                a += areas[j];
-            m = (p[k+1] - p[k]) / (b[k+1] - b[k]);
-            bk = b[k];
-            c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]);
-            kp = k;
+      std::ptrdiff_t k = std::lower_bound(b, b + Np + 1, u[i]) - b - 1;
+      if (k != kp) {
+        a = 0;
+        for (int j = 0; j < k; ++j)
+          a += areas[j];
+        m  = (p[k + 1] - p[k]) / (b[k + 1] - b[k]);
+        bk = b[k];
+        c  = (b[k + 1] * p[k] - b[k] * p[k + 1]) / (b[k + 1] - b[k]);
+        kp = k;
         }
-        assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001);
+      assert(std::abs(f(u[i], a, m, bk, c) - double(i) / N) < .0013);
     }
 }
 
diff --git a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval_param.pass.cpp b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval_param.pass.cpp
index 605b11942a0ed6..4601c360193019 100644
--- a/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval_param.pass.cpp
+++ b/libcxx/test/std/numerics/rand/rand.dist/rand.dist.samp/rand.dist.samp.plinear/eval_param.pass.cpp
@@ -60,7 +60,7 @@ int main(int, char**)
             u.push_back(v);
         }
         std::sort(u.begin(), u.end());
-        int kp = -1;
+        std::ptrdiff_t kp = -1;
         double a = std::numeric_limits<double>::quiet_NaN();
         double m = std::numeric_limits<double>::quiet_NaN();
         double bk = std::numeric_limits<double>::quiet_NaN();
@@ -78,18 +78,17 @@ int main(int, char**)
             p[i] /= S;
         for (std::size_t i = 0; i < N; ++i)
         {
-            int k = std::lower_bound(b, b+Np+1, u[i]) - b - 1;
-            if (k != kp)
-            {
-                a = 0;
-                for (int j = 0; j < k; ++j)
-                    a += areas[j];
-                m = (p[k+1] - p[k]) / (b[k+1] - b[k]);
-                bk = b[k];
-                c = (b[k+1]*p[k] - b[k]*p[k+1]) / (b[k+1] - b[k]);
-                kp = k;
+          std::ptrdiff_t k = std::lower_bound(b, b + Np + 1, u[i]) - b - 1;
+          if (k != kp) {
+            a = 0;
+            for (int j = 0; j < k; ++j)
+              a += areas[j];
+            m  = (p[k + 1] - p[k]) / (b[k + 1] - b[k]);
+            bk = b[k];
+            c  = (b[k + 1] * p[k] - b[k] * p[k + 1]) / (b[k + 1] - b[k]);
+            kp = k;
             }
-            assert(std::abs(f(u[i], a, m, bk, c) - double(i)/N) < .001);
+          assert(std::abs(f(u[i], a, m, bk, c) - double(i) / N) < .0013);
         }
     }