Update Non central T PDF:

Lot's more tests, especially in the tails.
Added Hypergeometric and Integration methods as fallbacks.

tools/non_central_t_pdf_data.cpp

@@ -0,0 +1,92 @@
+//  (C) Copyright John Maddock 2024.
+//  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)
+
+#define BOOST_MATH_MAX_SERIES_ITERATION_POLICY 10000000
+#define BOOST_MATH_USE_MPFR
+
+#include "mp_t.hpp"
+#include <boost/math/special_functions/hypergeometric_1F1.hpp>
+#include <boost/math/distributions/non_central_t.hpp>
+#include <boost/lexical_cast.hpp>
+#include <fstream>
+#include <map>
+#include <boost/math/tools/test_data.hpp>
+#include <boost/random.hpp>
+
+using namespace boost::math::tools;
+using namespace boost::math;
+using namespace std;
+
+struct nc_t_pdf_gen
+{
+   mp_t operator()(mp_t v, mp_t mu, mp_t x)
+   {
+      //
+      // Arbitrary smallest value we accept, below this, we will likely underflow to zero
+      // when computing at double precision:
+      //
+      static const mp_t minimum = 1e-270;
+
+      mp_t Av = boost::math::hypergeometric_1F1((v + 1) / 2, boost::math::constants::half<mp_t>(), mu * mu * x * x / (2 * (x * x + v)));
+      mp_t Bv = boost::math::hypergeometric_1F1(v / 2 + mp_t(1), mp_t(3) / 2, mu * mu * x * x / (2 * (x * x + v)));
+      Bv *= boost::math::tgamma_ratio(v / 2 + mp_t(1), (v + mp_t(1)) / 2);
+      Bv *= boost::math::constants::root_two<mp_t>() * mu * x / sqrt(x * x + v);
+
+      Av += Bv;
+      Av *= exp(-mu * mu / 2) * pow(1 + x * x / v, -(v + 1) / 2) * boost::math::tgamma_ratio((v + mp_t(1)) / 2, v / 2);
+      Av /= sqrt(v) * boost::math::constants::root_pi<mp_t>();
+
+      if (Av < minimum)
+         throw std::domain_error("Result too small!");
+
+      return Av;
+   }
+};
+
+
+int main(int, char* [])
+{
+   parameter_info<mp_t> arg1, arg2, arg3;
+   test_data<mp_t> data;
+
+   std::cout << "Welcome.\n"
+      "This program will generate spot tests for the non central t PDF:\n";
+
+   std::string line;
+   bool cont;
+
+   random_ns::mt19937 rnd;
+   random_ns::uniform_real_distribution<float> ur_a(0, 20);
+
+
+   do
+   {
+      if (0 == get_user_parameter_info(arg1, "v"))
+         return 1;
+      if (0 == get_user_parameter_info(arg2, "nc"))
+         return 1;
+
+      arg3 = make_periodic_param(mp_t(-20), mp_t(200), 170);
+
+      data.insert(nc_t_pdf_gen(), arg1, arg2, arg3);
+      std::cout << "Any more data [y/n]?";
+      std::getline(std::cin, line);
+      boost::algorithm::trim(line);
+      cont = (line == "y");
+   } while (cont);
+
+   std::cout << "Enter name of test data file [default=nc_t_pdf_data.ipp]";
+   std::getline(std::cin, line);
+   boost::algorithm::trim(line);
+   if (line == "")
+      line = "nc_t_pdf_data.ipp";
+   std::ofstream ofs(line.c_str());
+   ofs << std::scientific << std::setprecision(40);
+   write_code(ofs, data, line.c_str());
+
+   return 0;
+}
+
+