diff --git a/doc/distributions/beta.qbk b/doc/distributions/beta.qbk
index 3e1af3a6c..29dcbb307 100644
--- a/doc/distributions/beta.qbk
+++ b/doc/distributions/beta.qbk
@@ -45,18 +45,6 @@
         RealType probability); // probability cdf.
    };
    
-   RealType mean(const beta_distribution<RealType>& dist);
-     // Mean of beta distribution = a/(a+b).
-   RealType variance(const beta_distribution<RealType>& dist);
-     // Variance of beta distribution = a * b / (a+b)^2 * (a + b + 1).
-   RealType mode(const beta_distribution<RealType>& dist);
-     // Mode of beta distribution = (a-1) / (a + b + 2)
-   RealType skewness(const beta_distribution<RealType>& dist);
-     // Skewness of beta distribution = 2 (b-a) sqrt(a+b+1)/(a+b+2) * sqrt(a * b)
-   RealType kurtosis(const beta_distribution<RealType>& dist);
-   RealType kurtosis_excess(const beta_distribution<RealType>& dist);
-   // See below.
-   
    }} // namespaces
    
 The class type `beta_distribution` represents a 
@@ -72,16 +60,6 @@ See also:
 [@http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/BetaDistribution.html beta distribution]
 and [@http://en.wikipedia.org/wiki/Bayesian_statistics Bayesian statistics].
 
-[h4 Member Functions]
-
-   beta_distribution(RealType alpha, RealType beta);
-
-Constructor example: beta_distribution<> mybeta22(2., 5);
-
-constructs a double beta distribution with two unequal shape parameters,
-whose pdf is shown in grey in the
-[@http://en.wikipedia.org/wiki/Beta_distribution plot].
-
 The [@http://en.wikipedia.org/wiki/Probability_density_function probability density function PDF]
 for the [@http://en.wikipedia.org/wiki/Beta_distribution beta distribution]
 defined on the interval \[0,1\] is given by:
@@ -90,14 +68,15 @@ f(x;[alpha],[beta]) = x[super[alpha] - 1] (1 - x)[super[beta] -1] / B([alpha], [
 
 where B([alpha], [beta]) is the
 [@http://en.wikipedia.org/wiki/Beta_function beta function],
-implemented in the Math Toolkit as __beta.  Division by the beta function
+implemented in this library as __beta.  Division by the beta function
 ensures that the pdf is normalized to the range zero to unity.
 
-[@http://en.wikipedia.org/wiki/Image:Beta_distribution_pdf.png Examples of pdf for various values of shape parameters are shown here.]
-x is a [@http://en.wikipedia.org/wiki/Random_variate random variate]
-in the interval zero to unity.
-Note the [alpha] = [beta] = 2 (purple line) is dome-shaped,
-and might be approximated by a symmetrical trianglar distribution.
+The following graph illustrates examples of the pdf for various values 
+of the shape parameters.  Note the [alpha] = [beta] = 2 (blue line) 
+is dome-shaped, and might be approximated by a symmetrical trianglar 
+distribution.
+
+[$../graphs/beta_dist.png]
 
 If [alpha] = [beta] = 1, then it is a __space
 [@http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 uniform distribution],
@@ -107,8 +86,22 @@ If [alpha] != [beta], then the shape is asymmetric
 and could be approximated by a triangle
 whose apex is away from the centre (where x = half).
 
-Accessor member functions simply retrieve the shape parameters,
-/alpha/ and /beta/ used to construct the distribution.
+[h4 Member Functions]
+
+[h5 Constructor]
+
+   beta_distribution(RealType alpha, RealType beta);
+
+Constructs a beta distribution with shape parameters /alpha/ and /beta/.
+
+For example: 
+   
+   beta_distribution<> mybeta(2, 5);
+   
+Constructs a the beta distribution with alpha=2 and beta=5 (shown in yellow
+in the graph above).
+
+[h5 Parameter Accessors]
 
    RealType alpha() const;
    
@@ -118,34 +111,65 @@ Returns the parameter /alpha/ from which this distribution was constructed.
    
 Returns the parameter /beta/ from which this distribution was constructed.
 
-So
+So for example:
 
-  mybeta25.alpha() == 2.;
-  mybeta25.beta() == 5.;
+   beta_distribution<> mybeta(2, 5);
+   assert(mybeta.alpha() == 2.);  // mybeta.alpha() returns 2
+   assert(mybeta.beta() == 5.);   // mybeta.beta()  returns 5
 
 [h4 Parameter Estimators]
 
 Two pairs of parameter estimators are provided.
 
-One estimates either [alpha] __space or [beta] __space from presumed-known mean and variance.
+One estimates either [alpha] __space or [beta] __space 
+from presumed-known mean and variance.
 
-The other pair estimates either [alpha] __space or [beta] __space from the cdf and x.
+The other pair estimates either [alpha] __space or [beta] __space from 
+the cdf and x.
 
-(It is also possible to estimate [alpha] __space and  [beta] __space from 'known' mode & quantile.
-For example, calculators are provided
-[@http://www.ausvet.com.au/pprev/content.php?page=PPscript Pooled Prevalance Calculator] and
+It is also possible to estimate [alpha] __space and  [beta] __space from 
+'known' mode & quantile.  For example, calculators are provided by the
+[@http://www.ausvet.com.au/pprev/content.php?page=PPscript 
+Pooled Prevalance Calculator] and
 [@http://www.epi.ucdavis.edu/diagnostictests/betabuster.html Beta Buster]
-but this is NOT (yet) implemented here).
+but this is not yet implemented here.
 
+      static RealType estimate_alpha(
+        RealType mean, // Expected value of mean.
+        RealType variance); // Expected value of variance.
+        
+Returns the unique value of [alpha][space] that corresponds to a 
+beta distribution with mean /mean/ and variance /variance/.
+      
+      static RealType estimate_beta(
+        RealType mean, // Expected value of mean.
+        RealType variance); // Expected value of variance.
+  
+Returns the unique value of [beta][space] that corresponds to a 
+beta distribution with mean /mean/ and variance /variance/.
+      
+      static RealType estimate_alpha(
+        RealType beta, // from beta.
+        RealType x, //  x.
+        RealType probability); // probability cdf
+        
+Returns the value of [alpha][space] that gives:
+`cdf(beta_distribution<RealType>(alpha, beta), x) == probability`.
+      
+      static RealType estimate_beta(
+        RealType alpha, // alpha.
+        RealType x, // probability x.
+        RealType probability); // probability cdf.
 
+Returns the value of [beta][space] that gives:
+`cdf(beta_distribution<RealType>(alpha, beta), x) == probability`.
+      
 [h4 Non-member Accessor Functions]
 
 All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
 that are generic to all distributions are supported: __usual_accessors.
 
-The formulae for calculating these are shown as comments above
-(and in the table below) with the exception of the __kurtosis and __kurtosis_excess 
-whose formula is difficult to show as a comment but is given below, and at
+The formulae for calculating these are shown in the table below, and at
 [@http://mathworld.wolfram.com/BetaDistribution.html Wolfram Mathworld].
 
 [h4 Applications]
@@ -185,22 +209,23 @@ please refer to these functions for information on accuracy.
 
 [h4 Implementation]
 
-In the following table /p/ is the probablity and /q = 1-p/.
+In the following table /a/ and /b/ are the parameters [alpha][space] and [beta],
+/x/ is the random variable, /p/ is the probablity and /q = 1-p/.
 
 [table
 [[Function][Implementation Notes]]
-[[pdf][`pow(x, (a-1)) * pow((1 - x), (b-1))/ beta(a, b)`]]
-[[cdf][inverse incomplete beta function `ibeta(a, b, x)`]]
-[[cdf complement][`1 - ibeta(a, b, x)`]]
-[[quantile][inverse incomplete beta function `ibeta_inv(a, b, p)`]]
-[[quantile from the complement][inverse incomplete beta function complement `ibetac_inv(a, b, q)`]]
+[[pdf][f(x;[alpha],[beta]) = x[super[alpha] - 1] (1 - x)[super[beta] -1] / B([alpha], [beta])\n\n
+      Implemented using __ibeta_derivative(a, b, x).]]
+[[cdf][Using the incomplete beta function __ibeta(a, b, x)]]
+[[cdf complement][__ibetac(a, b, x)]]
+[[quantile][Using the inverse incomplete beta function __ibeta_inv(a, b, p)]]
+[[quantile from the complement][__ibetac_inv(a, b, q)]]
 [[mean][`a/(a+b)`]]
 [[variance][`a * b / (a+b)^2 * (a + b + 1)`]]
 [[mode][`(a-1) / (a + b + 2)`]]
 [[skewness][`2 (b-a) sqrt(a+b+1)/(a+b+2) * sqrt(a * b)`]]
-[[kurtosis][`3 + 6 * a * a * a - a * a * (2 * b -1) + b * b * (b + 1) - 2 * a * b * (b + 2) /
-        a * b * (a + b + 2) * (a + b + 3)`]]
-[[kurtosis excess][`kurtosis - 3`]]
+[[kurtosis excess][ [$../equations/beta_dist_kurtosis.png]  ]]
+[[kurtosis][`kurtosis + 3`]]
 [[parameter estimation][ ]]
 [[alpha\n
 from mean and variance][`mean * (( (mean * (1 - mean)) / variance)- 1)`]]
@@ -209,7 +234,7 @@ from mean and variance][`(1 - mean) * (((mean * (1 - mean)) /variance)-1)`]]
 [[The member functions `estimate_alpha` and `estimate_beta`\n
   from cdf and probability x\n
   and *either* `alpha` or `beta`][Implemented in terms of the inverse incomplete beta functions\n
-__ibetac_inv, __ibeta_inv, and __ibetac_invb respectively.]]
+__ibeta_inva, and __ibeta_invb respectively.]]
 [[`estimate_alpha`][`ibeta_inva(beta, x, probability)`]]
 [[`estimate_beta`][`ibeta_invb(alpha, x, probability)`]]
 ]
diff --git a/doc/equations/beta_dist_kurtosis.png b/doc/equations/beta_dist_kurtosis.png
new file mode 100644
index 000000000..1be258bfd
Binary files /dev/null and b/doc/equations/beta_dist_kurtosis.png differ
diff --git a/doc/equations/dist_reference.xml b/doc/equations/dist_reference.xml
index 0cb28c4a0..d85c2c92e 100644
--- a/doc/equations/dist_reference.xml
+++ b/doc/equations/dist_reference.xml
@@ -997,5 +997,76 @@
     </msup>
   </mrow>
 </math>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+  <mrow>
+    <mn>6</mn>
+    <mfrac>
+      <mrow>
+        <msup>
+          <mi>&alpha;</mi>
+          <mn>3</mn>
+        </msup>
+        <mo>&minus;</mo>
+        <msup>
+          <mi>&alpha;</mi>
+          <mn>2</mn>
+        </msup>
+        <mfenced>
+          <mrow>
+            <mn>2</mn>
+            <mi>&beta;</mi>
+            <mo>&minus;</mo>
+            <mn>1</mn>
+          </mrow>
+        </mfenced>
+        <mo>+</mo>
+        <msup>
+          <mi>&beta;</mi>
+          <mn>2</mn>
+        </msup>
+        <mfenced>
+          <mrow>
+            <mi>&beta;</mi>
+            <mo>&minus;</mo>
+            <mn>1</mn>
+          </mrow>
+        </mfenced>
+        <mo>&minus;</mo>
+        <mn>2</mn>
+        <mi>&alpha;</mi>
+        <mi>&beta;</mi>
+        <mfenced>
+          <mrow>
+            <mi>&beta;</mi>
+            <mo>+</mo>
+            <mn>2</mn>
+          </mrow>
+        </mfenced>
+      </mrow>
+      <mrow>
+        <mi>&alpha;</mi>
+        <mi>&beta;</mi>
+        <mfenced>
+          <mrow>
+            <mi>&alpha;</mi>
+            <mo>+</mo>
+            <mi>&beta;</mi>
+            <mo>+</mo>
+            <mn>2</mn>
+          </mrow>
+        </mfenced>
+        <mfenced>
+          <mrow>
+            <mi>&alpha;</mi>
+            <mo>+</mo>
+            <mi>&beta;</mi>
+            <mo>+</mo>
+            <mn>3</mn>
+          </mrow>
+        </mfenced>
+      </mrow>
+    </mfrac>
+  </mrow>
+</math>
 </body>
 </html>
\ No newline at end of file
diff --git a/doc/graphs/beta_dist.png b/doc/graphs/beta_dist.png
new file mode 100644
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diff --git a/doc/graphs/beta_dist.ps b/doc/graphs/beta_dist.ps
new file mode 100644
index 000000000..5bf74bb4e
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diff --git a/include/boost/math/distributions/beta.hpp b/include/boost/math/distributions/beta.hpp
index 2d492c6ec..7fc7dda6b 100644
--- a/include/boost/math/distributions/beta.hpp
+++ b/include/boost/math/distributions/beta.hpp
@@ -46,11 +46,11 @@ namespace boost
       template <class RealType>
       inline bool check_alpha(const char* function, const RealType& alpha, RealType* result)
       {
-        if(!(boost::math::isfinite)(alpha) || (alpha < 0))
+        if(!(boost::math::isfinite)(alpha) || (alpha <= 0))
         {
           *result = tools::domain_error<RealType>(
             function,
-            "Alpha argument is %1%, but must be >= 0 !", alpha);
+            "Alpha argument is %1%, but must be > 0 !", alpha);
           return false;
         }
         return true;
@@ -59,11 +59,11 @@ namespace boost
       template <class RealType>
       inline bool check_beta(const char* function, const RealType& beta, RealType* result)
       {
-        if(!(boost::math::isfinite)(beta) || (beta < 0))
+        if(!(boost::math::isfinite)(beta) || (beta <= 0))
         {
           *result = tools::domain_error<RealType>(
             function,
-            "Beta argument is %1%, but must be >= 0 !", beta);
+            "Beta argument is %1%, but must be > 0 !", beta);
           return false;
         }
         return true;
@@ -119,11 +119,11 @@ namespace boost
       template <class RealType>
       inline bool check_mean(const char* function, const RealType& mean, RealType* result)
       {
-        if(!(boost::math::isfinite)(mean) || (mean < 0))
+        if(!(boost::math::isfinite)(mean) || (mean <= 0))
         {
           *result = tools::domain_error<RealType>(
             function,
-            "mean argument is %1%, but must be >= 0 !", mean);
+            "mean argument is %1%, but must be > 0 !", mean);
           return false;
         }
         return true;
@@ -131,11 +131,11 @@ namespace boost
       template <class RealType>
       inline bool check_variance(const char* function, const RealType& variance, RealType* result)
       {
-        if(!(boost::math::isfinite)(variance) || (variance < 0))
+        if(!(boost::math::isfinite)(variance) || (variance <= 0))
         {
           *result = tools::domain_error<RealType>(
             function,
-            "variance argument is %1%, but must be >= 0 !", variance);
+            "variance argument is %1%, but must be > 0 !", variance);
           return false;
         }
         return true;
@@ -314,24 +314,23 @@ namespace boost
       return (2 * (b-a) * sqrt(a + b + 1)) / ((a + b + 2) * sqrt(a * b));
     } // skewness
 
-    template <class RealType>
-    inline RealType kurtosis(const beta_distribution<RealType>& dist)
-    {
-      RealType a = dist.alpha();
-      RealType b = dist.beta();
-      return 3 + 6 * a * a * a - a * a * (2 * b -1) + b * b * (b + 1) - 2 * a * b * (b + 2) /
-        a * b * (a + b + 2) * (a + b + 3);
-    } // kurtosis
-
     template <class RealType>
     inline RealType kurtosis_excess(const beta_distribution<RealType>& dist)
     {
       RealType a = dist.alpha();
       RealType b = dist.beta();
-      return 6 * a * a * a - a * a * (2 * b -1) + b * b * (b + 1) - 2 * a * b * (b + 2) /
-        a * b * (a + b + 2) * (a + b + 3);
+      RealType a_2 = a * a;
+      RealType n = 6 * (a_2 * a - a_2 * (2 * b - 1) + b * b * (b + 1) - 2 * a * b * (b + 2));
+      RealType d = a * b * (a + b + 2) * (a + b + 3);
+      return  n / d;
     } // kurtosis_excess
 
+    template <class RealType>
+    inline RealType kurtosis(const beta_distribution<RealType>& dist)
+    {
+      return 3 + kurtosis_excess(dist);
+    } // kurtosis
+
     template <class RealType>
     RealType pdf(const beta_distribution<RealType>& dist, const RealType x)
     { // Probability Density/Mass Function.
@@ -353,7 +352,7 @@ namespace boost
         return result;
       }
       using boost::math::beta;
-      return pow(x, (a-1)) * pow((1 - x), (b-1))/ beta(a, b);
+      return ibeta_derivative(a, b, x);
     } // pdf
 
     template <class RealType>
@@ -418,7 +417,7 @@ namespace boost
       // Calculate cdf beta using the incomplete beta function.
       // Use of ibeta here prevents cancellation errors in calculating
       // 1 - x if x is very small, perhaps smaller than machine epsilon.
-      return 1 - ibeta(a, b, x);
+      return ibetac(a, b, x);
     } // beta cdf
 
     template <class RealType>
diff --git a/include/boost/math/special_functions/beta.hpp b/include/boost/math/special_functions/beta.hpp
index 15552ae99..1153de280 100644
--- a/include/boost/math/special_functions/beta.hpp
+++ b/include/boost/math/special_functions/beta.hpp
@@ -808,6 +808,15 @@ T ibeta_imp(T a, T b, T x, const L& l, bool inv, bool normalised)
    T fract;
    T y = 1 - x;
 
+   if(normalised)
+   {
+      // extend to a few very special cases:
+      if((a == 0) && (b != 0))
+         return inv ? 0 : 1;
+      else if(b == 0)
+         return inv ? 1 : 0;
+   }
+
    if(a <= 0)
       tools::domain_error<T>(BOOST_CURRENT_FUNCTION, "The argument a to the incomplete beta function must be greater than zero (got a=%1%).", a);
    if(b <= 0)
@@ -1061,12 +1070,12 @@ T ibeta_derivative_imp(T a, T b, T x, const L& l)
    if(x == 0)
    {
       return (a > 1) ? 0 : 
-         (a == 1) ? 1 : tools::overflow_error<T>(BOOST_CURRENT_FUNCTION, 0);
+         (a == 1) ? 1 / boost::math::beta(a, b) : tools::overflow_error<T>(BOOST_CURRENT_FUNCTION, 0);
    }
    else if(x == 1)
    {
       return (b > 1) ? 0 :
-         (b == 1) ? 1 : tools::overflow_error<T>(BOOST_CURRENT_FUNCTION, 0);
+         (b == 1) ? 1 / boost::math::beta(a, b) : tools::overflow_error<T>(BOOST_CURRENT_FUNCTION, 0);
    }
    //
    // Now the regular cases:
diff --git a/test/test_beta_dist.cpp b/test/test_beta_dist.cpp
index 7f37be653..78aa7369e 100644
--- a/test/test_beta_dist.cpp
+++ b/test/test_beta_dist.cpp
@@ -196,10 +196,11 @@ void test_spots(RealType)
      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
      static_cast<RealType>(0)),  // x
      static_cast<RealType>(1));
-  BOOST_CHECK_EQUAL(
+  BOOST_CHECK_CLOSE_FRACTION(
      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
      static_cast<RealType>(0.5)),  // x
-     static_cast<RealType>(1));
+     static_cast<RealType>(1),
+     tolerance);
 
   BOOST_CHECK_EQUAL(
      beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)).alpha(),
@@ -225,14 +226,14 @@ void test_spots(RealType)
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
      static_cast<RealType>(0.1)),  // x
-     static_cast<RealType>(0.02800000000000000000000000000000000000000), // Seems exact.
+     static_cast<RealType>(0.02800000000000000000000000000000000000000L), // Seems exact.
      // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.1&a=2&b=2&digits=40
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
      static_cast<RealType>(0.0001)),  // x
-     static_cast<RealType>(2.999800000000000000000000000000000000000e-8),
+     static_cast<RealType>(2.999800000000000000000000000000000000000e-8L),
      // http://members.aol.com/iandjmsmith/BETAEX.HTM 2.9998000000004
      // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.0001&a=2&b=2&digits=40
       tolerance);
@@ -241,41 +242,42 @@ void test_spots(RealType)
   BOOST_CHECK_CLOSE_FRACTION(
      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
      static_cast<RealType>(0.0001)),  // x
-     static_cast<RealType>(0.0005999400000000004), // http://members.aol.com/iandjmsmith/BETAEX.HTM
-      tolerance);
+     static_cast<RealType>(0.0005999400000000004L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
+     // Slightly higher tolerance for real concept:
+     (std::numeric_limits<RealType>::is_specialized ? 1 : 10) * tolerance);  
 
 
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
      static_cast<RealType>(0.9999)),  // x
-     static_cast<RealType>(0.999999970002), // http://members.aol.com/iandjmsmith/BETAEX.HTM
+     static_cast<RealType>(0.999999970002L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
      // Wolfram 0.9999999700020000000000000000000000000000
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(2)),
      static_cast<RealType>(0.9)),  // x
-     static_cast<RealType>(0.9961174629530394895796514664963063381217), 
+     static_cast<RealType>(0.9961174629530394895796514664963063381217L), 
      // Wolfram
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
      static_cast<RealType>(0.1)),  // x
-     static_cast<RealType>(0.2048327646991334516491978475505189480977), 
+     static_cast<RealType>(0.2048327646991334516491978475505189480977L), 
      // Wolfram
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
      static_cast<RealType>(0.9)),  // x
-     static_cast<RealType>(0.7951672353008665483508021524494810519023), 
+     static_cast<RealType>(0.7951672353008665483508021524494810519023L), 
      // Wolfram
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
-     static_cast<RealType>(0.7951672353008665483508021524494810519023)),  // x
+     static_cast<RealType>(0.7951672353008665483508021524494810519023L)),  // x
      static_cast<RealType>(0.9), 
      // Wolfram
      tolerance);
@@ -283,13 +285,13 @@ void test_spots(RealType)
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
      static_cast<RealType>(0.6)),  // x
-     static_cast<RealType>(0.5640942168489749316118742861695149357858), 
+     static_cast<RealType>(0.5640942168489749316118742861695149357858L), 
      // Wolfram
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
-     static_cast<RealType>(0.5640942168489749316118742861695149357858)),  // x
+     static_cast<RealType>(0.5640942168489749316118742861695149357858L)),  // x
      static_cast<RealType>(0.6), 
      // Wolfram
       tolerance); 
@@ -298,13 +300,13 @@ void test_spots(RealType)
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
      static_cast<RealType>(0.6)),  // x
-     static_cast<RealType>(0.1778078083562213736802876784474931812329), 
+     static_cast<RealType>(0.1778078083562213736802876784474931812329L), 
      // Wolfram
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
-     static_cast<RealType>(0.1778078083562213736802876784474931812329)),  // x
+     static_cast<RealType>(0.1778078083562213736802876784474931812329L)),  // x
      static_cast<RealType>(0.6), 
      // Wolfram
       tolerance); // gives 
@@ -326,13 +328,13 @@ void test_spots(RealType)
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(complement(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
      static_cast<RealType>(0.1))),  // complement of x
-     static_cast<RealType>(0.7951672353008665483508021524494810519023), 
+     static_cast<RealType>(0.7951672353008665483508021524494810519023L), 
      // Wolfram
       tolerance);
 
     BOOST_CHECK_CLOSE_FRACTION(
      quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
-     static_cast<RealType>(0.0280000000000000000000000000000000000)),  // x
+     static_cast<RealType>(0.0280000000000000000000000000000000000L)),  // x
      static_cast<RealType>(0.1), 
      // Wolfram
       tolerance);
@@ -341,14 +343,14 @@ void test_spots(RealType)
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(complement(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
      static_cast<RealType>(0.1))),  // x
-     static_cast<RealType>(0.9720000000000000000000000000000000000000), // Exact.
+     static_cast<RealType>(0.9720000000000000000000000000000000000000L), // Exact.
      // Wolfram
       tolerance);
 
   BOOST_CHECK_CLOSE_FRACTION(
      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
      static_cast<RealType>(0.9999)),  // x
-     static_cast<RealType>(0.0005999399999999344), // http://members.aol.com/iandjmsmith/BETAEX.HTM
+     static_cast<RealType>(0.0005999399999999344L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
       tolerance*10); // Note less accurate.
 
   //void test_spot(
@@ -374,8 +376,8 @@ void test_spots(RealType)
      static_cast<RealType>(2),   // alpha a
      static_cast<RealType>(2),   // beta b
      static_cast<RealType>(0.1), // Probability  p
-     static_cast<RealType>(0.0280000000000000000000000000000000000), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1 - 0.0280000000000000000000000000000000000),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(0.0280000000000000000000000000000000000L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1 - 0.0280000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
 
@@ -399,56 +401,56 @@ void test_spots(RealType)
      static_cast<RealType>(2),   // alpha a
      static_cast<RealType>(2),   // beta b
      static_cast<RealType>(0.01), // Probability  p
-     static_cast<RealType>(0.0002980000000000000000000000000000000000000), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1-0.0002980000000000000000000000000000000000000),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(0.0002980000000000000000000000000000000000000L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1-0.0002980000000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
   test_spot(
      static_cast<RealType>(2),   // alpha a
      static_cast<RealType>(2),   // beta b
      static_cast<RealType>(0.001), // Probability  p
-     static_cast<RealType>(2.998000000000000000000000000000000000000E-6), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1-2.998000000000000000000000000000000000000E-6),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(2.998000000000000000000000000000000000000E-6L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1-2.998000000000000000000000000000000000000E-6L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
   test_spot(
      static_cast<RealType>(2),   // alpha a
      static_cast<RealType>(2),   // beta b
      static_cast<RealType>(0.0001), // Probability  p
-     static_cast<RealType>(2.999800000000000000000000000000000000000E-8), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1-2.999800000000000000000000000000000000000E-8),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(2.999800000000000000000000000000000000000E-8L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1-2.999800000000000000000000000000000000000E-8L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
   test_spot(
      static_cast<RealType>(2),   // alpha a
      static_cast<RealType>(2),   // beta b
      static_cast<RealType>(0.99), // Probability  p
-     static_cast<RealType>(0.9997020000000000000000000000000000000000), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1-0.9997020000000000000000000000000000000000),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(0.9997020000000000000000000000000000000000L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1-0.9997020000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
   test_spot(
      static_cast<RealType>(0.5),   // alpha a
      static_cast<RealType>(2),   // beta b
      static_cast<RealType>(0.5), // Probability  p
-     static_cast<RealType>(0.8838834764831844055010554526310612991060), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1-0.8838834764831844055010554526310612991060),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(0.8838834764831844055010554526310612991060L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1-0.8838834764831844055010554526310612991060L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
   test_spot(
      static_cast<RealType>(0.5),   // alpha a
      static_cast<RealType>(3.),   // beta b
      static_cast<RealType>(0.7), // Probability  p
-     static_cast<RealType>(0.9903963064097119299191611355232156905687), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1-0.9903963064097119299191611355232156905687),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(0.9903963064097119299191611355232156905687L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1-0.9903963064097119299191611355232156905687L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
   test_spot(
      static_cast<RealType>(0.5),   // alpha a
      static_cast<RealType>(3.),   // beta b
      static_cast<RealType>(0.1), // Probability  p
-     static_cast<RealType>(0.5545844446520295253493059553548880128511), // Probability of result (CDF of beta), P
-     static_cast<RealType>(1-0.5545844446520295253493059553548880128511),  // Complement of CDF Q = 1 - P
+     static_cast<RealType>(0.5545844446520295253493059553548880128511L), // Probability of result (CDF of beta), P
+     static_cast<RealType>(1-0.5545844446520295253493059553548880128511L),  // Complement of CDF Q = 1 - P
      tolerance); // Test tolerance.
 
 } // template <class RealType>void test_spots(RealType)
@@ -462,99 +464,96 @@ int test_main(int, char* [])
 #endif
 
 
-	// Check that can generate beta distribution using one convenience methods:
-	beta_distribution<> mybeta11(1., 1.); // Using default RealType double.
-  // but that
-	//boost::math::beta mybeta1(1., 1.); // Using typedef fails.
-  // error C2039: 'beta' : is not a member of 'boost::math'
+   // Check that can generate beta distribution using one convenience methods:
+   beta_distribution<> mybeta11(1., 1.); // Using default RealType double.
+   // but that
+   // boost::math::beta mybeta1(1., 1.); // Using typedef fails.
+   // error C2039: 'beta' : is not a member of 'boost::math'
 
-  // Basic sanity-check spot values.
+   // Basic sanity-check spot values.
 
-  // Some simple checks using double only.
-  BOOST_CHECK_EQUAL(mybeta11.alpha(), 1); // 
-  BOOST_CHECK_EQUAL(mybeta11.beta(), 1);
-  BOOST_CHECK_EQUAL(mean(mybeta11), 0.5); // 1 / (1 + 1) = 1/2 exactly
-  BOOST_CHECK_THROW(mode(mybeta11), std::domain_error);
-	beta_distribution<> mybeta22(2., 2.); // pdf is dome shape.
-  BOOST_CHECK_EQUAL(mode(mybeta22), 0.5); // 2-1 / (2+2-2) = 1/2 exactly.
-	beta_distribution<> mybetaH2(0.5, 2.); // 
-	beta_distribution<> mybetaH3(0.5, 3.); // 
+   // Some simple checks using double only.
+   BOOST_CHECK_EQUAL(mybeta11.alpha(), 1); // 
+   BOOST_CHECK_EQUAL(mybeta11.beta(), 1);
+   BOOST_CHECK_EQUAL(mean(mybeta11), 0.5); // 1 / (1 + 1) = 1/2 exactly
+   BOOST_CHECK_THROW(mode(mybeta11), std::domain_error);
+   beta_distribution<> mybeta22(2., 2.); // pdf is dome shape.
+   BOOST_CHECK_EQUAL(mode(mybeta22), 0.5); // 2-1 / (2+2-2) = 1/2 exactly.
+   beta_distribution<> mybetaH2(0.5, 2.); // 
+   beta_distribution<> mybetaH3(0.5, 3.); // 
 
 
-  // Check a few values using double.
-  BOOST_CHECK_EQUAL(pdf(mybeta11, 1), 1); // is uniform unity over 0 to 1,
-  BOOST_CHECK_EQUAL(pdf(mybeta11, 0), 1); // including zero and unity.
-  BOOST_CHECK_EQUAL(pdf(mybeta11, 0.5), 1);
-  BOOST_CHECK_EQUAL(pdf(mybeta11, 0.0001), 1);
-  BOOST_CHECK_EQUAL(pdf(mybeta11, 0.9999), 1);
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.1), 0.1, std::numeric_limits<double>::epsilon());
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.5), 0.5, std::numeric_limits<double>::epsilon());
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.9), 0.9, std::numeric_limits<double>::epsilon());
-  BOOST_CHECK_EQUAL(cdf(mybeta11, 1), 1.); // Exact unity expected.
+   // Check a few values using double.
+   BOOST_CHECK_EQUAL(pdf(mybeta11, 1), 1); // is uniform unity over 0 to 1,
+   BOOST_CHECK_EQUAL(pdf(mybeta11, 0), 1); // including zero and unity.
+   // Although these next three have an exact result, internally they're
+   // *not* treated as special cases, and may be out by a couple of eps:
+   BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.5), 1.0, 5*std::numeric_limits<double>::epsilon());
+   BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.0001), 1.0, 5*std::numeric_limits<double>::epsilon());
+   BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.9999), 1.0, 5*std::numeric_limits<double>::epsilon());
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.1), 0.1, std::numeric_limits<double>::epsilon());
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.5), 0.5, std::numeric_limits<double>::epsilon());
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.9), 0.9, std::numeric_limits<double>::epsilon());
+   BOOST_CHECK_EQUAL(cdf(mybeta11, 1), 1.); // Exact unity expected.
 
-  double tol = std::numeric_limits<double>::epsilon() * 10;
-  BOOST_CHECK_EQUAL(pdf(mybeta22, 1), 0); // is dome shape.
-  BOOST_CHECK_EQUAL(pdf(mybeta22, 0), 0);
-  BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.5), 1.5, tol); // top of dome, expect exactly 3/2.
-  BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.0001), 5.9994000000000E-4, tol);
-  BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.9999), 5.9994000000000E-4, tol*50);
+   double tol = std::numeric_limits<double>::epsilon() * 10;
+   BOOST_CHECK_EQUAL(pdf(mybeta22, 1), 0); // is dome shape.
+   BOOST_CHECK_EQUAL(pdf(mybeta22, 0), 0);
+   BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.5), 1.5, tol); // top of dome, expect exactly 3/2.
+   BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.0001), 5.9994000000000E-4, tol);
+   BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.9999), 5.9994000000000E-4, tol*50);
 
-  BOOST_CHECK_EQUAL(cdf(mybeta22, 0.), 0); // cdf is a curved line from 0 to 1.
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.028000000000000, tol);
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.5), 0.5, tol);
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.9), 0.972000000000000, tol);
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.0001), 2.999800000000000000000000000000000000000E-8, tol);
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.001), 2.998000000000000000000000000000000000000E-6, tol);
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.01), 0.0002980000000000000000000000000000000000000, tol);
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.02800000000000000000000000000000000000000, tol); // exact
-  BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.99), 0.9997020000000000000000000000000000000000, tol);
+   BOOST_CHECK_EQUAL(cdf(mybeta22, 0.), 0); // cdf is a curved line from 0 to 1.
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.028000000000000, tol);
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.5), 0.5, tol);
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.9), 0.972000000000000, tol);
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.0001), 2.999800000000000000000000000000000000000E-8, tol);
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.001), 2.998000000000000000000000000000000000000E-6, tol);
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.01), 0.0002980000000000000000000000000000000000000, tol);
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.02800000000000000000000000000000000000000, tol); // exact
+   BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.99), 0.9997020000000000000000000000000000000000, tol);
 
-  BOOST_CHECK_EQUAL(cdf(mybeta22, 1), 1.); // Exact unity expected.
+   BOOST_CHECK_EQUAL(cdf(mybeta22, 1), 1.); // Exact unity expected.
 
-  // Complement
+   // Complement
 
-  BOOST_CHECK_CLOSE_FRACTION(cdf(complement(mybeta22, 0.9)), 0.028000000000000, tol);
+   BOOST_CHECK_CLOSE_FRACTION(cdf(complement(mybeta22, 0.9)), 0.028000000000000, tol);
 
-  // quantile.
-  BOOST_CHECK_CLOSE_FRACTION(quantile(mybeta22, 0.028), 0.1, tol); 
-  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(mybeta22, 1 - 0.028)), 0.1, tol);
-  BOOST_CHECK_EQUAL(kurtosis(mybeta11), 3+ kurtosis_excess(mybeta11)); // Check kurtosis_excess = kurtosis - 3;
-  BOOST_CHECK_CLOSE_FRACTION(variance(mybeta22), 0.05, tol);
-  BOOST_CHECK_CLOSE_FRACTION(mode(mybeta22), 0.5, tol);
-  BOOST_CHECK_CLOSE_FRACTION(mean(mybeta22), 0.5, tol);
+   // quantile.
+   BOOST_CHECK_CLOSE_FRACTION(quantile(mybeta22, 0.028), 0.1, tol); 
+   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(mybeta22, 1 - 0.028)), 0.1, tol);
+   BOOST_CHECK_EQUAL(kurtosis(mybeta11), 3+ kurtosis_excess(mybeta11)); // Check kurtosis_excess = kurtosis - 3;
+   BOOST_CHECK_CLOSE_FRACTION(variance(mybeta22), 0.05, tol);
+   BOOST_CHECK_CLOSE_FRACTION(mode(mybeta22), 0.5, tol);
+   BOOST_CHECK_CLOSE_FRACTION(mean(mybeta22), 0.5, tol);
+   BOOST_CHECK_CLOSE_FRACTION(skewness(mybeta22), 0.0, tol);
+   BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(mybeta22), -144.0 / 168, tol);
+   BOOST_CHECK_CLOSE_FRACTION(skewness(beta_distribution<>(3, 5)), 0.30983866769659335081434123198259, tol);
+
+   BOOST_CHECK_EQUAL(beta_distribution<double>::estimate_alpha(mean(mybeta22), variance(mybeta22)), mybeta22.alpha()); // mean, variance, probability. 
+   BOOST_CHECK_EQUAL(beta_distribution<double>::estimate_beta(mean(mybeta22), variance(mybeta22)), mybeta22.beta());// mean, variance, probability. 
+
+   BOOST_CHECK_CLOSE_FRACTION(mybeta22.estimate_alpha(mybeta22.beta(), 0.8, cdf(mybeta22, 0.8)), mybeta22.alpha(), tol);
+   BOOST_CHECK_CLOSE_FRACTION(mybeta22.estimate_beta(mybeta22.alpha(), 0.8, cdf(mybeta22, 0.8)), mybeta22.beta(), tol);
 
 
-   //cout << beta_distribution<double>::estimate_alpha(mean(mybeta22), variance(mybeta22)) << endl; // 2
-  //cout << beta_distribution<double>::estimate_beta(mean(mybeta22), variance(mybeta22)) << endl; // 2
-  BOOST_CHECK_EQUAL(beta_distribution<double>::estimate_alpha(mean(mybeta22), variance(mybeta22)), mybeta22.alpha()); // mean, variance, probability. 
-  BOOST_CHECK_EQUAL(beta_distribution<double>::estimate_beta(mean(mybeta22), variance(mybeta22)), mybeta22.beta());// mean, variance, probability. 
-
- // BOOST_CHECK_CLOSE_FRACTION(ibeta_inva(mybeta22.beta(), 0.8, cdf(mybeta22, 0.8)), mybeta22.alpha(), tol);
-  //BOOST_CHECK_CLOSE_FRACTION(ibeta_inva(mybeta22.beta(), 0.8, cdf(mybeta22, 0.8)), mybeta22.alpha(), tol);
-  BOOST_CHECK_CLOSE_FRACTION(mybeta22.estimate_alpha(mybeta22.beta(), 0.8, cdf(mybeta22, 0.8)), mybeta22.alpha(), tol);
-  BOOST_CHECK_CLOSE_FRACTION(mybeta22.estimate_beta(mybeta22.alpha(), 0.8, cdf(mybeta22, 0.8)), mybeta22.beta(), tol);
+   beta_distribution<real_concept> rcbeta22(2, 2); // Using RealType real_concept.
+   cout << "numeric_limits<real_concept>::is_specialized " << numeric_limits<real_concept>::is_specialized << endl;
+   cout << "numeric_limits<real_concept>::digits " << numeric_limits<real_concept>::digits << endl;
+   cout << "numeric_limits<real_concept>::digits10 " << numeric_limits<real_concept>::digits10 << endl;
+   cout << "numeric_limits<real_concept>::epsilon " << numeric_limits<real_concept>::epsilon() << endl;
 
 
-	beta_distribution<real_concept> rcbeta22(2, 2); // Using RealType real_concept.
-  cout << "numeric_limits<real_concept>::is_specialized " << numeric_limits<real_concept>::is_specialized << endl;
-  cout << "numeric_limits<real_concept>::digits " << numeric_limits<real_concept>::digits << endl;
-  cout << "numeric_limits<real_concept>::digits10 " << numeric_limits<real_concept>::digits10 << endl;
-  cout << "numeric_limits<real_concept>::epsilon " << numeric_limits<real_concept>::epsilon() << endl;
-
-  // Tests for improvements to Boost.test display of errors.
-  //BOOST_CHECK_CLOSE_FRACTION(rcbeta22.alpha(), static_cast<real_concept>(2 + 3 * std::numeric_limits<double>::epsilon()), 0);
-  //BOOST_CHECK_CLOSE_FRACTION(cdf(rcbeta22, 0.1), static_cast<real_concept>(0.028000000000009), 0);
-
-  // (Parameter value, arbitrarily zero, only communicates the floating point type).
-  test_spots(0.0F); // Test float.
-  test_spots(0.0); // Test double.
+   // (Parameter value, arbitrarily zero, only communicates the floating point type).
+   test_spots(0.0F); // Test float.
+   test_spots(0.0); // Test double.
 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
-  test_spots(0.0L); // Test long double.
+   test_spots(0.0L); // Test long double.
 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
-  test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 #endif
 #endif
-  return 0;
+   return 0;
 } // int test_main(int, char* [])
 
 /*