[Boost-bugs] [Boost C++ Libraries] #11557: cdf error with non-central chi-squared with ncp = 0

Subject: [Boost-bugs] [Boost C++ Libraries] #11557: cdf error with non-central chi-squared with ncp = 0
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2015-08-19 19:12:24

#11557: cdf error with non-central chi-squared with ncp = 0
------------------------------------+------------------------------
 Reporter:  Mark Abney <maabney@…>  |       Type:  Bugs
   Status:  new                     |  Milestone:  To Be Determined
Component:  None                    |    Version:  Boost 1.57.0
 Severity:  Problem                 |   Keywords:
------------------------------------+------------------------------
 The complement of the cdf of the non-central chi-squared distribution with
 non-centrality parameter = 0 should return the same value as the standard
 (i.e. central) chi-squared distribution. For ncp very small, this happens,
 but when ncp = 0 it returns the negative of the (non-complement) cdf.
 Example code:

 {{{
 #include <iostream>
 #include <boost/math/distributions.hpp>

 using std::cout;
 using std::cin;
 using std::endl;

 using boost::math::chi_squared;

 int main(int argc, char *argv[])
 {
     double df = 4, quantile = 12;
     cout << "df = " << df << endl;
     cout << "quantile = " << quantile << endl;

     chi_squared chi(df);
     cout << "chi.df = " << chi.degrees_of_freedom() << endl;
     cout << "P(X <= " << quantile << ") = " << cdf(chi, quantile) << endl;
     cout << "P(X > " << quantile << ") = " << cdf(complement(chi,
 quantile)) << endl;

     double ncp1 = 1e-300;
     double ncp2 = 0;

     boost::math::non_central_chi_squared nchi1(df, ncp1);
     boost::math::non_central_chi_squared nchi2(df, ncp2);
     cout << "nchi1.df = " << nchi1.degrees_of_freedom()
          << "; nchi1.ncp = " << nchi1.non_centrality() << endl;
     cout << "P(X <= " << quantile << ") = " << cdf(nchi1, quantile) <<
 endl;
     cout << "P(X > " << quantile << ") = " << cdf(complement(nchi1,
 quantile)) << endl;
     cout << "nchi2.df = " << nchi2.degrees_of_freedom()
          << "; nchi2.ncp = " << nchi2.non_centrality() << endl;
     cout << "P(X <= " << quantile << ") = " << cdf(nchi2, quantile) <<
 endl;
     cout << "P(X > " << quantile << ") = " << cdf(complement(nchi2,
 quantile)) << endl;

     return 0;
 }

 }}}

 Note the output lines P(X > 12), which should all be equal. In the first
 two cases this is correct, but in the last one P(X > 12) = - P(X <= 12),
 which is necessarily wrong.

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/11557>
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