diff --git a/test/test_cauchy.cpp b/test/test_cauchy.cpp
index 38bf168ca..43498cc5b 100644
--- a/test/test_cauchy.cpp
+++ b/test/test_cauchy.cpp
@@ -640,16 +640,19 @@ void test_spots(RealType T)
          static_cast<RealType>(-3),  // probability.
 			tolerance); // %
 
-   //
-   // Things that are errors:
-   //
-   cauchy_distribution<RealType> dist;
-   BOOST_CHECK_THROW(
-       mean(dist),
-       std::domain_error);
+   cauchy_distribution<RealType> dist; // default (0, 1)
    BOOST_CHECK_EQUAL(
        mode(dist),
        static_cast<RealType>(0));
+   BOOST_CHECK_EQUAL(
+       median(dist),
+       static_cast<RealType>(0));
+   //
+   // Things that are errors:
+   //
+   BOOST_CHECK_THROW(
+       mean(dist),
+       std::domain_error);
    BOOST_CHECK_THROW(
        variance(dist),
        std::domain_error);
diff --git a/test/test_chi_squared.cpp b/test/test_chi_squared.cpp
index 651d8e696..5d96ea927 100644
--- a/test/test_chi_squared.cpp
+++ b/test/test_chi_squared.cpp
@@ -404,6 +404,12 @@ void test_spots(RealType)
     BOOST_CHECK_CLOSE(
        mode(dist)
        , static_cast<RealType>(6), tol2);
+
+    BOOST_CHECK_CLOSE(
+       median(dist), 
+       quantile(
+          chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+          static_cast<RealType>(0.5)), static_cast<RealType>(1)); // 1% - approximate.
     // skewness:
     BOOST_CHECK_CLOSE(
        skewness(dist)
diff --git a/test/test_exponential_dist.cpp b/test/test_exponential_dist.cpp
index d232aa9e9..1062d54be 100644
--- a/test/test_exponential_dist.cpp
+++ b/test/test_exponential_dist.cpp
@@ -208,6 +208,13 @@ void test_spots(RealType T)
          exponential_distribution<RealType>(2)),
          static_cast<RealType>(0),           
 			tolerance); // %
+
+   BOOST_CHECK_CLOSE(
+      ::boost::math::median(
+         exponential_distribution<RealType>(4)),
+         static_cast<RealType>(0.693147180559945309417232121458176568075500134360255254) / 4,           
+			tolerance); // %
+
    BOOST_CHECK_CLOSE(
       ::boost::math::skewness(
          exponential_distribution<RealType>(2)),
diff --git a/test/test_extreme_value.cpp b/test/test_extreme_value.cpp
index 748684801..d91a5aac0 100644
--- a/test/test_extreme_value.cpp
+++ b/test/test_extreme_value.cpp
@@ -5,7 +5,7 @@
 // (See accompanying file LICENSE_1_0.txt
 // or copy at http://www.boost.org/LICENSE_1_0.txt)
 
-// test_students_t.cpp
+// test_extreme_value.cpp
 
 #define BOOST_MATH_THROW_ON_DOMAIN_ERROR
 #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
@@ -27,7 +27,6 @@
 #include <boost/test/included/test_exec_monitor.hpp> // Boost.Test
 #include <boost/test/floating_point_comparison.hpp>
 
-
 #include <iostream>
 	using std::cout;
 	using std::endl;
@@ -146,6 +145,12 @@ void test_spots(RealType T)
          extreme_value_distribution<RealType>(2, 3)),
          static_cast<RealType>(2),           
 			tolerance); // %
+   BOOST_CHECK_CLOSE(
+      ::boost::math::median(
+         extreme_value_distribution<RealType>(0, 1)),
+         static_cast<RealType>(+0.36651292058166432701243915823266946945426344783710526305367771367056),           
+			tolerance); // %
+
    BOOST_CHECK_CLOSE(
       ::boost::math::skewness(
          extreme_value_distribution<RealType>(2, 3)),
diff --git a/test/test_fisher_f.cpp b/test/test_fisher_f.cpp
index 67330fcb6..172232598 100644
--- a/test/test_fisher_f.cpp
+++ b/test/test_fisher_f.cpp
@@ -204,7 +204,6 @@ void test_spots(RealType)
   // pretty useless, but it is an excellent sanity check.
 
   RealType tolerance = 0.002f * 100;
-
   cout << "Tolerance = " << tolerance << "%." << endl;
 
   using boost::math::fisher_f_distribution;
@@ -370,8 +369,7 @@ void test_spots(RealType)
 
 // These might allow some further cross checks?
 
-
-    RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100;  // 5eps as a percent
+    RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100;  // 5 eps as a percent
     cout << "Tolerance = " << tol2 << "%." << endl;
     fisher_f_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(6));
     RealType x = 7;
@@ -510,6 +508,10 @@ void test_spots(RealType)
           fisher_f_distribution<RealType>(8, 8),
           static_cast<RealType>(1.1))), std::domain_error
        );
+    // median NOT implemented.
+    BOOST_CHECK_THROW(
+       median(fisher_f_distribution<RealType>(8, 8)), std::domain_error);
+
 } // template <class RealType>void test_spots(RealType)
 
 int test_main(int, char* [])
diff --git a/test/test_gamma_dist.cpp b/test/test_gamma_dist.cpp
index 8f7267f8c..7ef82529d 100644
--- a/test/test_gamma_dist.cpp
+++ b/test/test_gamma_dist.cpp
@@ -221,6 +221,10 @@ void test_spots(RealType T)
        kurtosis_excess(dist)
        , 6 / static_cast<RealType>(8), tol2);
 
+    BOOST_CHECK_CLOSE(
+       median(dist), static_cast<RealType>(23.007748327502412), tol2);
+    // Rely on default definition in derived accessors.
+
 } // template <class RealType>void test_spots(RealType)
 
 int test_main(int, char* [])
@@ -245,3 +249,20 @@ int test_main(int, char* [])
 } // int test_main(int, char* [])
 
 
+/*
+
+Output:
+
+Running 1 test case...
+Tolerance for type float is 0.000238419 %
+Tolerance for type float is 0.001 %
+Tolerance for type double is 5e-012 %
+Tolerance for type double is 0.001 %
+Tolerance for type long double is 5e-012 %
+Tolerance for type long double is 0.001 %
+Tolerance for type class boost::math::concepts::real_concept is 5e-012 %
+Tolerance for type class boost::math::concepts::real_concept is 0.001 %
+*** No errors detected
+
+
+*/
\ No newline at end of file
diff --git a/test/test_lognormal.cpp b/test/test_lognormal.cpp
index 5392577ff..96f675f50 100644
--- a/test/test_lognormal.cpp
+++ b/test/test_lognormal.cpp
@@ -220,6 +220,15 @@ void test_spots(RealType T)
    BOOST_CHECK_CLOSE(
     mode(dist)
     , static_cast<RealType>(0.36787944117144232159552377016146L), tolerance);
+
+   BOOST_CHECK_CLOSE(
+    median(dist)
+    , static_cast<RealType>(exp(dist.location())), tolerance);
+
+   BOOST_CHECK_CLOSE(
+    median(dist),
+    quantile(dist, static_cast<RealType>(0.5)), tolerance);
+
    // skewness:
    BOOST_CHECK_CLOSE(
     skewness(dist)
diff --git a/test/test_negative_binomial.cpp b/test/test_negative_binomial.cpp
index a673131c4..369b5ba74 100644
--- a/test/test_negative_binomial.cpp
+++ b/test/test_negative_binomial.cpp
@@ -716,6 +716,12 @@ if(std::numeric_limits<RealType>::is_specialized)
   static_cast<RealType>(0)), std::domain_error
   );
   // End of check throwing 'duff' out-of-domain values.
+
+  BOOST_CHECK_THROW(
+  median( // NOT implemented.
+  negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25))),
+  std::domain_error);
+
   return;
 } // template <class RealType> void test_spots(RealType) // Any floating-point type RealType.
 
@@ -734,14 +740,14 @@ int test_main(int, char* [])
 #endif
 
 #ifdef BOOST_MATH_THROW_ON_OVERFLOW_ERROR
-  cout << "BOOST_MATH_THROW_ON_OVERFLOW_ERROR" << " is defined to throw on domain error." << endl;
+  cout << "BOOST_MATH_THROW_ON_OVERFLOW_ERROR" << " is defined to throw on overflow error." << endl;
 #else
-  cout << "BOOST_MATH_THROW_ON_OVERFLOW_ERROR" << " is NOT defined, so NO throw on domain error." << endl;
+  cout << "BOOST_MATH_THROW_ON_OVERFLOW_ERROR" << " is NOT defined, so NO throw on overflow error." << endl;
 #endif
 #ifdef BOOST_MATH_THROW_ON_UNDERFLOW_ERROR
-  cout << "BOOST_MATH_THROW_ON_UNDERFLOW_ERROR" << " is defined to throw on domain error." << endl;
+  cout << "BOOST_MATH_THROW_ON_UNDERFLOW_ERROR" << " is defined to throw on underflow error." << endl;
 #else
-  cout << "BOOST_MATH_THROW_ON_UNDERFLOW_ERROR" << " is NOT defined, so NO throw on domain error." << endl;
+  cout << "BOOST_MATH_THROW_ON_UNDERFLOW_ERROR" << " is NOT defined, so NO throw on underflow error." << endl;
 #endif
   // Test some simple double only examples.
   negative_binomial_distribution<double> my8dist(8., 0.25);
@@ -765,15 +771,14 @@ int test_main(int, char* [])
 
 /*
 
------- Build started: Project: test_negative_binomial, Configuration: Debug Win32 ------
 Compiling...
 test_negative_binomial.cpp
 Linking...
 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_negative_binomial.exe"
 Running 1 test case...
 BOOST_MATH_THROW_ON_DOMAIN_ERROR is defined to throw on domain error.
-BOOST_MATH_THROW_ON_OVERFLOW_ERROR is NOT defined, so NO throw on domain error.
-BOOST_MATH_THROW_ON_UNDERFLOW_ERROR is NOT defined, so NO throw on domain error.
+BOOST_MATH_THROW_ON_OVERFLOW_ERROR is NOT defined, so NO throw on overflow error.
+BOOST_MATH_THROW_ON_UNDERFLOW_ERROR is NOT defined, so NO throw on underflow error.
 Tolerance = 0.0119209%.
 Tolerance 5 eps = 5.96046e-007%.
 Tolerance = 2.22045e-011%.
@@ -783,8 +788,5 @@ Tolerance 5 eps = 1.11022e-015%.
 Tolerance = 2.22045e-011%.
 Tolerance 5 eps = 1.11022e-015%.
 *** No errors detected
-Build Time 0:08
-Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\test_negative_binomial\Debug\BuildLog.htm"
-test_negative_binomial - 0 error(s), 0 warning(s)
 
 */
diff --git a/test/test_normal.cpp b/test/test_normal.cpp
index 8c81b058b..ce124f2bd 100644
--- a/test/test_normal.cpp
+++ b/test/test_normal.cpp
@@ -223,6 +223,11 @@ void test_spots(RealType T)
     BOOST_CHECK_CLOSE(
        mode(dist)
        , static_cast<RealType>(8), tol2);
+
+    BOOST_CHECK_CLOSE(
+       median(dist)
+       , static_cast<RealType>(8), tol2);
+
     // skewness:
     BOOST_CHECK_CLOSE(
        skewness(dist)
diff --git a/test/test_poisson.cpp b/test/test_poisson.cpp
index 41ce9f294..c1edd1a7e 100644
--- a/test/test_poisson.cpp
+++ b/test/test_poisson.cpp
@@ -143,6 +143,23 @@ void test_spots(RealType)
       std::domain_error);
 
   // Check some test values.
+
+  BOOST_CHECK_CLOSE( // mode
+     mode(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
+      static_cast<RealType>(4), // mode.
+			tolerance);
+
+  //BOOST_CHECK_CLOSE( // mode
+  //   median(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
+  //    static_cast<RealType>(4), // mode.
+		//	tolerance);
+  poisson_distribution<RealType> dist4(static_cast<RealType>(40));
+
+  BOOST_CHECK_CLOSE( // median
+     median(dist4), // mode = mean = 4. median = 40.328333333333333 
+      quantile(dist4, static_cast<RealType>(0.5)), // 39.332839138842637
+			tolerance);
+
   // PDF
   BOOST_CHECK_CLOSE(
      pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
@@ -319,7 +336,7 @@ void test_spots(RealType)
          tolerance/5); // 
 
   // EQUAL is too optimistic - fails [5.0000000000000124 != 5]
-  //BOOST_CHECK_EQUAL(boost::math::quantile( // 
+  // BOOST_CHECK_EQUAL(boost::math::quantile( // 
   //       poisson_distribution<RealType>(5.),  // mean.
   //       static_cast<RealType>(0.615960654833065)),  //  probability.
   //       static_cast<RealType>(5.)); // Expect k = 5 events.
@@ -330,6 +347,55 @@ void test_spots(RealType)
          static_cast<RealType>(5.), // Expect k = 5 events.
          tolerance/5); 
 
+  // Check on quantile of other examples of inverse of cdf.
+  BOOST_CHECK_CLOSE( 
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(10.)), // mean
+      static_cast<RealType>(10)),  // k events. 
+      static_cast<RealType>(0.5830397501929856), // probability.
+			tolerance);
+
+  BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
+         poisson_distribution<RealType>(10.),  // mean.
+         static_cast<RealType>(0.5830397501929856)),  //  probability.
+         static_cast<RealType>(10.), // Expect k = 10 events.
+         tolerance/5); 
+
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
+      static_cast<RealType>(5)),  // k events. 
+      static_cast<RealType>(0.785130387030406), // probability.
+			tolerance);
+
+  BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
+         poisson_distribution<RealType>(4.),  // mean.
+         static_cast<RealType>(0.785130387030406)),  //  probability.
+         static_cast<RealType>(5.), // Expect k = 10 events.
+         tolerance/5); 
+
+
+
+  //BOOST_CHECK_CLOSE(boost::math::quantile(
+  //       poisson_distribution<RealType>(5),  // mean.
+  //       static_cast<RealType>(0.785130387030406)),  //  probability.
+  //        // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
+  //       static_cast<RealType>(6.), // Expect k = 6 events. 
+  //       tolerance/5); 
+
+  //BOOST_CHECK_CLOSE(boost::math::quantile(
+  //       poisson_distribution<RealType>(5),  // mean.
+  //       static_cast<RealType>(0.77)),  //  probability.
+  //        // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
+  //       static_cast<RealType>(7.), // Expect k = 6 events. 
+  //       tolerance/5); 
+
+  //BOOST_CHECK_CLOSE(boost::math::quantile(
+  //       poisson_distribution<RealType>(5),  // mean.
+  //       static_cast<RealType>(0.75)),  //  probability.
+  //        // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
+  //       static_cast<RealType>(6.), // Expect k = 6 events. 
+  //       tolerance/5); 
+
   BOOST_CHECK_CLOSE(
     boost::math::quantile(
          complement(
@@ -441,11 +507,21 @@ int test_main(int, char* [])
 
      cout << endl;
   }
+
    cout << cdf(poisson_distribution<double>(5), static_cast<double>(0)) << ' ' << endl; // 0.006737946999085467
    cout << cdf(poisson_distribution<double>(5), static_cast<double>(1)) << ' ' << endl; // 0.040427681994512805
    cout << cdf(poisson_distribution<double>(2), static_cast<double>(3)) << ' ' << endl; // 0.85712346049854715 
 #endif
 
+   {
+     for (int i = 1; i < 100; i++)
+     {
+       poisson_distribution<double> distn(static_cast<double>(i));
+       cout << i << ' ' << median(distn) << ' ' << quantile(distn, 0.5) << ' ' 
+         << median(distn) - quantile(distn, 0.5) << endl;
+     }
+   }
+
 	// (Parameter value, arbitrarily zero, only communicates the floating-point type).
   test_spots(0.0F); // Test float.
 	test_spots(0.0); // Test double.
diff --git a/test/test_triangular.cpp b/test/test_triangular.cpp
index dfd21417f..5362b3e20 100644
--- a/test/test_triangular.cpp
+++ b/test/test_triangular.cpp
@@ -458,6 +458,8 @@ void test_spots(RealType T)
   BOOST_CHECK_CLOSE_FRACTION(
     mode(distu01), static_cast<RealType>(0), tolerance);
   // skewness:
+  BOOST_CHECK_CLOSE_FRACTION(
+    median(trim12), static_cast<RealType>(-0.13397459621556151), tolerance);
   BOOST_CHECK_EQUAL(
     skewness(distu01), static_cast<RealType>(0));
   // kertosis:
@@ -528,6 +530,8 @@ int test_main(int, char* [])
   BOOST_CHECK_EQUAL(tristd.mode(), 0);
   BOOST_CHECK_EQUAL(tristd.upper(), 1);
 
+  cout <<  median(tristd) << endl;
+
   triangular_distribution<> tri011(0, 1, 1); // Using default RealType double.
   // mode is upper
   BOOST_CHECK_EQUAL(tri011.lower(), 0); // Check defaults again.
@@ -611,6 +615,7 @@ int test_main(int, char* [])
     BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.));
     BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5), quantile(complement(*dist, 0.5)),  tol5eps); // OK
     BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98), quantile(complement(*dist, 1. - 0.98)),tol5eps);
+    // cout << setprecision(17) <<  median(*dist) << endl;
   }
 
   cout << showpos << setprecision(2) << endl;
@@ -635,10 +640,6 @@ int test_main(int, char* [])
     BOOST_CHECK_CLOSE_FRACTION(quantile(trim12, dx), quantile(complement(trim12, 1 - dx)), tol500eps);
   }
   cout << endl;
-
-
-
-
   // Basic sanity-check spot values.
   // (Parameter value, arbitrarily zero, only communicates the floating point type).
   test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
@@ -662,26 +663,27 @@ int test_main(int, char* [])
 
 Output:
 
------- Build started: Project: test_triangular, Configuration: Debug Win32 ------
 Compiling...
 test_triangular.cpp
 Linking...
 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_triangular.exe"
 Running 1 test case...
+0
 Distribution 0
+0
 Distribution 1
+1
 Distribution 2
+0.35355339059327373
 Distribution 3
+0.5
 Distribution 4
+-0.13397459621556151
 Tolerance for type float is 5.96046e-007.
 Tolerance for type double is 1.11022e-015.
 Tolerance for type long double is 1.11022e-015.
 Tolerance for type class boost::math::concepts::real_concept is 1.11022e-015.
 *** No errors detected
-Build Time 0:05
-Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\test_triangular\Debug\BuildLog.htm"
-test_triangular - 0 error(s), 0 warning(s)
-========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
 
 
 
diff --git a/test/test_uniform.cpp b/test/test_uniform.cpp
index 159123035..ab1d942b2 100644
--- a/test/test_uniform.cpp
+++ b/test/test_uniform.cpp
@@ -320,6 +320,8 @@ void test_spots(RealType T)
    // mode:
    BOOST_CHECK_CLOSE_FRACTION(
     mode(distu01), static_cast<RealType>(0), tolerance);
+   BOOST_CHECK_CLOSE_FRACTION(
+      median(distu01), static_cast<RealType>(0.5), tolerance);
    // skewness:
    BOOST_CHECK_EQUAL(
     skewness(distu01), static_cast<RealType>(0));
diff --git a/test/test_weibull.cpp b/test/test_weibull.cpp
index 2618f4ab1..b34ea0d56 100644
--- a/test/test_weibull.cpp
+++ b/test/test_weibull.cpp
@@ -296,6 +296,10 @@ void test_spots(RealType T)
    BOOST_CHECK_CLOSE(
     mode(dist)
     , dist.scale() * pow((dist.shape() - 1) / dist.shape(), 1/dist.shape()), tolerance);
+   // median:
+   BOOST_CHECK_CLOSE(
+    median(dist)
+    , dist.scale() * pow(log(static_cast<RealType>(2)), 1 / dist.shape()), tolerance);
    // skewness:
    BOOST_CHECK_CLOSE(
     skewness(dist),