id	summary	reporter	owner	description	type	status	milestone	component	version	severity	resolution	keywords	cc
9183	quantile for poisson distribution - precision issue?	tan@…	John Maddock	"The following (there are others) returns an ""unexpected"" result:

#define BOOST_MATH_DISCRETE_QUANTILE_POLICY integer_round_up
// #define BOOST_MATH_DISCRETE_QUANTILE_POLICY real

#include <cstdlib>
#include <cstdio>

#include <boost/math/distributions/poisson.hpp>

int main()
{
   double m=54.3;
   double x=66.0;

   boost::math::poisson_distribution<> dist( m );

   std::printf(
         ""\nqpois(ppois(66,54.3),54.3) = %d\n\n"",
         boost::math::quantile(
               dist,
               boost::math::cdf( dist, x ) ) );

   return 0
}

The ""expected"" answer is 66 but 67 is being returned.

I am aware of Ticket 8308 (https://svn.boost.org/trac/boost/ticket/8308).  I do not think R is ""rounding to the nearest"", and as far as I am aware, it has been consistent with

   quantile(p)=infimum {x|cdf(x)>=p}

which is what ""we"" needed/expected.

If we change the policy to give real output---on my Ubuntu 12.04 (Intel 14.0 C++ with g++ 4.7.3), the result is 6.600000000000001e+01.  So I wonder if this is just a (finite) precision/rounding issue ... in that it is really 66 to some ""fuzz"".

I have (also) tried this with revision 86054 of the trunk.

Thank you!"	Support Requests	closed	To Be Determined	math	Boost 1.54.0	Showstopper	fixed