Fix for issue #800

include/boost/math/distributions/non_central_t.hpp

@@ -578,11 +578,11 @@ namespace boost
             BOOST_MATH_STD_USING
             if ((boost::math::isinf)(v))
             {
-               return 3;
+               return 1;
             }
             if (delta == 0)
             { // == Student's t
-              return 3;
+              return 1;
             }
             T mean = boost::math::detail::mean(v, delta, pol);
             T l2 = delta * delta;
@@ -592,6 +592,7 @@ namespace boost
             result *= -mean * mean;
             result += v * v * (l2 * l2 + 6 * l2 + 3) / ((v - 4) * (v - 2));
             result /= var * var;
+            result -= static_cast<T>(3);
             return result;
          }
 

test/Jamfile.v2

@@ -889,7 +889,7 @@ test-suite distribution_tests :
    [ run complex_test.cpp ../../test/build//boost_unit_test_framework  ]
 
    [ compile test_dist_deduction_guides.cpp : [ requires cpp_deduction_guides cpp_variadic_templates ] ]
-
+   [ run git_issue_800.cpp ../../test/build//boost_unit_test_framework  ]
 ;
 
 test-suite mp :

test/git_issue_800.cpp

@@ -0,0 +1,33 @@
+// Copyright Matt Borland, 2022
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include "math_unit_test.hpp"
+#include <boost/math/distributions/non_central_t.hpp>
+
+template <typename T>
+void test()
+{
+    boost::math::non_central_t_distribution<T> nct(T(10), T(3));
+
+    // https://www.wolframalpha.com/input?i2d=true&i=N%5C%2891%29Kurtosis%5C%2891%29NoncentralStudentTDistribution%5C%2891%2910%5C%2844%29+3%5C%2893%29%5C%2893%29%5C%2844%2930%5C%2893%29
+    CHECK_MOLLIFIED_CLOSE(boost::math::kurtosis(nct), T(5.44234533171835241424739188827L), 1e-6);
+
+    boost::math::non_central_t_distribution<T> nct0(T(10), T(0));
+
+    // https://www.wolframalpha.com/input?i2d=true&i=Kurtosis%5C%2891%29NoncentralStudentTDistribution%5C%2891%2910%5C%2844%29+0%5C%2893%29%5C%2893%29
+    CHECK_ULP_CLOSE(boost::math::kurtosis(nct0), T(4), 1);
+
+    // https://www.wolframalpha.com/input?i2d=true&i=ExcessKurtosis%5C%2891%29NoncentralStudentTDistribution%5C%2891%2910%5C%2844%29+0%5C%2893%29%5C%2893%29
+    CHECK_ULP_CLOSE(boost::math::kurtosis_excess(nct0), T(1), 1);
+}
+
+int main(void)
+{
+    test<float>();
+    test<double>();
+    test<long double>();
+
+    return boost::math::test::report_errors();
+}

test/test_nc_t.hpp

@@ -107,7 +107,7 @@ RealType naive_kurtosis_excess(RealType v, RealType delta)
       / ((-4 + v) * (-2 + v));
    r /= (1 + delta*delta)*v / (-2 + v) - delta*delta*v *tgr*tgr / 2;
    r /= (1 + delta*delta)*v / (-2 + v) - delta*delta*v *tgr*tgr / 2;
-   return r;
+   return r - static_cast<RealType>(3);
 }
 
 float naive_kurtosis_excess(float v, float delta)
@@ -139,7 +139,7 @@ void test_spot(
       BOOST_CHECK_CLOSE(
          skewness(dist), naive_skewness(df, ncp), tol * 10 * tolerance_tgamma_extra);
       BOOST_CHECK_CLOSE(
-         kurtosis_excess(dist), naive_kurtosis_excess(df, ncp), tol * 50 * tolerance_tgamma_extra);
+         kurtosis_excess(dist), naive_kurtosis_excess(df, ncp), tol * 350 * tolerance_tgamma_extra);
       BOOST_CHECK_CLOSE(
          kurtosis(dist), 3 + naive_kurtosis_excess(df, ncp), tol * 50 * tolerance_tgamma_extra);
    }
@@ -517,8 +517,8 @@ void test_big_df(RealType)
       BOOST_CHECK_EQUAL(variance(maxdf), 1);
       BOOST_CHECK_EQUAL(skewness(infdf), 0);
       BOOST_CHECK_EQUAL(skewness(maxdf), 0);
-      BOOST_CHECK_EQUAL(kurtosis_excess(infdf), 3);
+      BOOST_CHECK_EQUAL(kurtosis_excess(infdf), 1);
-      BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(maxdf), static_cast<RealType>(3), tolerance);
+      BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(maxdf), static_cast<RealType>(1), tolerance);
 
       // Bad df examples.
 #ifndef BOOST_NO_EXCEPTIONS