Ticket #8837 (closed Bugs: fixed)
boost::math::students_t quantile() fails for huge degrees of freedom
|Reported by:||Paul McClellan <paulm@…>||Owned by:||johnmaddock|
|Milestone:||To Be Determined||Component:||math|
Student's t quantile function calls policies::raise_rounding_error() in iround() when degrees of freedom = 4503599627370496.
boost::math::students_t students(4503599627370496); double dRes = quantile(students, 0.4);
If this is disabled using #define BOOST_MATH_ROUNDING_ERROR_POLICY ignore_error in user.hpp the computation will continue.
The function inverse_students_t_hill() uses the test ndf > 1e20 to use the Standard Normal approximation, but Boost subsequently attempts to refine the estimate using the Halley step in fast_students_t_quantile_imp() and this becomes unreliable and eventually fails for huge dof such as dof = DBL_MAX (results in completely wrong result) or +Infinity (returns a NaN).
For consistency, I suggest the quantile function us the same threshold as pdf() and cdf() to approximate the Student's t with the standard normal distribution when dof > 1/eps.
I will attempt to attach my user.hpp file.