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Fix student's T for quantile of very small values. #1437

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jzmaddock merged 2 commits into from
Aug 26, 2026
+27 −2
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Fix student's T for quantile of very small values. #1437

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c37dd12
Fix student's T for quantile of very small values.
jzmaddock Aug 25, 2026
364cd3b
Students T: Add more test coverage.
jzmaddock Aug 26, 2026
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2 changes: 1 addition & 1 deletion include/boost/math/distributions/students_t.hpp
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Expand Up @@ -466,7 +466,7 @@ BOOST_MATH_GPU_ENABLED RealType calculate_hill_df_guess(
RealType za = quantile(complement(n, alpha));
RealType zb = quantile(complement(n, beta));

RealType v_norm = pow((za + zb) * sd / difference_from_mean, 2) - 1;
RealType v_norm = static_cast<RealType>(pow((za + zb) * sd / difference_from_mean, 2) - 1);
RealType hint = v_norm + (za * za - za * zb + zb * zb + 1) / 2;

return (hint <= 0) ? RealType(1) : hint;
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9 changes: 8 additions & 1 deletion include/boost/math/special_functions/detail/t_distribution_inv.hpp
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Expand Up @@ -509,7 +509,14 @@ BOOST_MATH_GPU_ENABLED T fast_students_t_quantile_imp(T df, T p, const Policy& p
// Get cdf from incomplete beta result:
T p0 = f0 / 2 - p;
// Get pdf from derivative:
T p1 = f1 * sqrt(y * xb * xb * xb / df);
T rxb = sqrt(xb);
T p1 = f1 * sqrt(y / df);
p1 *= rxb;
p1 *= rxb;
p1 *= rxb;
// If p1 has underflowed, all subsequent calculations will fail:
if (p1 < tools::min_value<T>())
return t;
//
// Second derivative divided by p1:
//
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18 changes: 18 additions & 0 deletions test/test_students_t.cpp
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Expand Up @@ -422,6 +422,24 @@ void test_spots(RealType)
BOOST_CHECK_THROW(boost::math::quantile(students_t_distribution<RealType>((std::numeric_limits<RealType>::min)() / 2), static_cast<RealType>(0.0025f)), std::overflow_error);
}
BOOST_CHECK_CLOSE(boost::math::cdf(students_t_distribution<RealType>(static_cast<RealType>(1)), ldexp(RealType(1), -30)), static_cast<RealType>(0.5000000002964491827262478614651948102240210317156775562512071908L), tolerance);
// https://github.com/boostorg/math/issues/1436
// We have quite limited precision in this area:
if (boost::math::tools::digits<RealType>() > boost::math::tools::digits<float>())
{
using std::ldexp;
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType>(static_cast<RealType>(3)), ldexp(RealType(1), -800)), static_cast<RealType>(-1.94452005735447553162080266906e+80L), 1e-8);
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType>(static_cast<RealType>(3)), ldexp(RealType(1), -1000)), static_cast<RealType>(-2.27760708321880957407749124767e+100L), 1e-8);
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType>(static_cast<RealType>(5)), ldexp(RealType(1), -1000)), static_cast<RealType>(-2.52030967154944272146770707689e+60L), 1e-8);
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType>(static_cast<RealType>(7)), ldexp(RealType(1), -1000)), static_cast<RealType>(-2.02884419021075115948274137329e+43L), 1e-8);
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType>(static_cast<RealType>(10)), ldexp(RealType(1), -1000)), static_cast<RealType>(-3.25092256692541451558538754799e+30L), 1e-8);
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType>(static_cast<RealType>(30)), ldexp(RealType(1), -1000)), static_cast<RealType>(-54306462721.8246714347211540407L), 1e-8);
using nopromote = boost::math::policies::policy<boost::math::policies::promote_double<false>>;
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType, nopromote>(static_cast<RealType>(30)), ldexp(RealType(1), -1000)), static_cast<RealType>(-54306462721.8246714347211540407L), 1e-8);
if (boost::math::tools::digits<RealType>() > boost::math::tools::digits<double>())
{
BOOST_CHECK_CLOSE_FRACTION(boost::math::quantile(students_t_distribution<RealType>(static_cast<RealType>(30)), ldexp(RealType(1), -16000)), static_cast<RealType>(-1.77766265021682828433490865393e+161L), 1e-8);
}
}
}

// Student's t pdf tests.
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