John Maddock — Sat, 16 Nov 2013 11:43:26 GMT

Oh :(

At present I don't know how to fix that without breaking other things, I need to think about this some more, it's possible too that it's basically unfixable without completely hammering the efficiency.

anonymous — Tue, 19 Nov 2013 14:00:25 GMT

Oops, just realized that I am "anonymous" ... so never got any indication that you have replied.

Thank you for thinking about it.

Tue, 26 Nov 2013 00:06:32 GMT

Hi John,

When computing the lower tail probabilities (inverse cdf) I set the rounding policy to integer_round_down, and when computing the upper tail probabilities (inverse survival function) I set the rounding policy to integer_round_up. This seems most consistent in the context of lower or upper tail tests.

In my very limited testing, when I use these rounding policies for hypergeometric quantiles I find I get the most accurate, or at least the most consistent, results in boost::math if I set the fudge_factor defined in hypergeometric_quantile_imp() an passed to round_x_from_p() to 1. That is, I remove the fudge_factor from the computations.

Perhaps this can help suggest an approach to this issue.

Best regards, Paul

Sat, 30 Nov 2013 22:09:47 GMT

John,

Here are some examples illustrating the effect of setting the fudge_factor to 1 with different quantile policies (thank you Anonymous).

#include "stdafx.h"
#define BOOST_MATH_DISCRETE_QUANTILE_POLICY integer_round_down
#include <cstdio>
#include <boost/math/distributions/hypergeometric.hpp>
int main()
{
   unsigned int xmin = 0;
   unsigned int length = 9;
   boost::math::hypergeometric_distribution<> dist( 8u, 8u, 16u );
   for ( unsigned int i = 0; i < length; ++i )
   {
      double x = xmin + i;
      double y =
         boost::math::cdf( dist, x );
         // boost::math::cdf( boost::math::complement( dist, x ) );
      std::printf(
            " x = %g\tCDF(x) = %f\tinverse-CDF(CDF(x)) = %g\n",
            x, y, boost::math::quantile( dist, y ) );
   }
   return 0;
}

With fudge_factor unchanged, and quantile policy integer_round_down I get:

 x = 0	CDF(x) = 0.000078	inverse-CDF(CDF(x)) = 0
 x = 1	CDF(x) = 0.005051	inverse-CDF(CDF(x)) = 0 <--
 x = 2	CDF(x) = 0.065967	inverse-CDF(CDF(x)) = 1 <--
 x = 3	CDF(x) = 0.309635	inverse-CDF(CDF(x)) = 2 <--
 x = 4	CDF(x) = 0.690365	inverse-CDF(CDF(x)) = 3 <--
 x = 5	CDF(x) = 0.934033	inverse-CDF(CDF(x)) = 4 <--
 x = 6	CDF(x) = 0.994949	inverse-CDF(CDF(x)) = 5 <--
 x = 7	CDF(x) = 0.999922	inverse-CDF(CDF(x)) = 7
 x = 8	CDF(x) = 1.000000	inverse-CDF(CDF(x)) = 8

Changing the quantile policy to integer_round_up I get:

 x = 0	CDF(x) = 0.000078	inverse-CDF(CDF(x)) = 1 <--
 x = 1	CDF(x) = 0.005051	inverse-CDF(CDF(x)) = 2 <--
 x = 2	CDF(x) = 0.065967	inverse-CDF(CDF(x)) = 3 <--
 x = 3	CDF(x) = 0.309635	inverse-CDF(CDF(x)) = 4 <--
 x = 4	CDF(x) = 0.690365	inverse-CDF(CDF(x)) = 5 <--
 x = 5	CDF(x) = 0.934033	inverse-CDF(CDF(x)) = 6 <--
 x = 6	CDF(x) = 0.994949	inverse-CDF(CDF(x)) = 7 <--
 x = 7	CDF(x) = 0.999922	inverse-CDF(CDF(x)) = 8 <--
 x = 8	CDF(x) = 1.000000	inverse-CDF(CDF(x)) = 8

However, if I force fudge_factor to 1.0 in hypergeometric_quantile.hpp, then with quantile policy integer_round_down I get:

 x = 0	CDF(x) = 0.000078	inverse-CDF(CDF(x)) = 0
 x = 1	CDF(x) = 0.005051	inverse-CDF(CDF(x)) = 1
 x = 2	CDF(x) = 0.065967	inverse-CDF(CDF(x)) = 2
 x = 3	CDF(x) = 0.309635	inverse-CDF(CDF(x)) = 3
 x = 4	CDF(x) = 0.690365	inverse-CDF(CDF(x)) = 4
 x = 5	CDF(x) = 0.934033	inverse-CDF(CDF(x)) = 5
 x = 6	CDF(x) = 0.994949	inverse-CDF(CDF(x)) = 5 <--
 x = 7	CDF(x) = 0.999922	inverse-CDF(CDF(x)) = 7
 x = 8	CDF(x) = 1.000000	inverse-CDF(CDF(x)) = 8

and with quantile policy integer_round_up I get:

 x = 0	CDF(x) = 0.000078	inverse-CDF(CDF(x)) = 0
 x = 1	CDF(x) = 0.005051	inverse-CDF(CDF(x)) = 1
 x = 2	CDF(x) = 0.065967	inverse-CDF(CDF(x)) = 2
 x = 3	CDF(x) = 0.309635	inverse-CDF(CDF(x)) = 4 <--
 x = 4	CDF(x) = 0.690365	inverse-CDF(CDF(x)) = 4
 x = 5	CDF(x) = 0.934033	inverse-CDF(CDF(x)) = 5
 x = 6	CDF(x) = 0.994949	inverse-CDF(CDF(x)) = 6
 x = 7	CDF(x) = 0.999922	inverse-CDF(CDF(x)) = 8 <--
 x = 8	CDF(x) = 1.000000	inverse-CDF(CDF(x)) = 8

John Maddock — Tue, 11 Mar 2014 17:06:35 GMT

Just to say I haven't forgotten this, I will get to it eventually!

Boost C++ Libraries: Ticket #9393: quantile for hypergeometric distribution - precision/rounding issue