diff any/include/boost/math/distributions/negative_binomial.hpp @ 160:cff480c41f97

Add some cross-platform Boost headers

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/any/include/boost/math/distributions/negative_binomial.hpp	Sat Feb 16 16:31:25 2019 +0000
@@ -0,0 +1,607 @@
+// boost\math\special_functions\negative_binomial.hpp
+
+// Copyright Paul A. Bristow 2007.
+// Copyright John Maddock 2007.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+// http://en.wikipedia.org/wiki/negative_binomial_distribution
+// http://mathworld.wolfram.com/NegativeBinomialDistribution.html
+// http://documents.wolfram.com/teachersedition/Teacher/Statistics/DiscreteDistributions.html
+
+// The negative binomial distribution NegativeBinomialDistribution[n, p]
+// is the distribution of the number (k) of failures that occur in a sequence of trials before
+// r successes have occurred, where the probability of success in each trial is p.
+
+// In a sequence of Bernoulli trials or events
+// (independent, yes or no, succeed or fail) with success_fraction probability p,
+// negative_binomial is the probability that k or fewer failures
+// preceed the r th trial's success.
+// random variable k is the number of failures (NOT the probability).
+
+// Negative_binomial distribution is a discrete probability distribution.
+// But note that the negative binomial distribution
+// (like others including the binomial, Poisson & Bernoulli)
+// is strictly defined as a discrete function: only integral values of k are envisaged.
+// However because of the method of calculation using a continuous gamma function,
+// it is convenient to treat it as if a continous function,
+// and permit non-integral values of k.
+
+// However, by default the policy is to use discrete_quantile_policy.
+
+// To enforce the strict mathematical model, users should use conversion
+// on k outside this function to ensure that k is integral.
+
+// MATHCAD cumulative negative binomial pnbinom(k, n, p)
+
+// Implementation note: much greater speed, and perhaps greater accuracy,
+// might be achieved for extreme values by using a normal approximation.
+// This is NOT been tested or implemented.
+
+#ifndef BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP
+#define BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b).
+#include <boost/math/distributions/complement.hpp> // complement.
+#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error.
+#include <boost/math/special_functions/fpclassify.hpp> // isnan.
+#include <boost/math/tools/roots.hpp> // for root finding.
+#include <boost/math/distributions/detail/inv_discrete_quantile.hpp>
+
+#include <boost/type_traits/is_floating_point.hpp>
+#include <boost/type_traits/is_integral.hpp>
+#include <boost/type_traits/is_same.hpp>
+#include <boost/mpl/if.hpp>
+
+#include <limits> // using std::numeric_limits;
+#include <utility>
+
+#if defined (BOOST_MSVC)
+#  pragma warning(push)
+// This believed not now necessary, so commented out.
+//#  pragma warning(disable: 4702) // unreachable code.
+// in domain_error_imp in error_handling.
+#endif
+
+namespace boost
+{
+  namespace math
+  {
+    namespace negative_binomial_detail
+    {
+      // Common error checking routines for negative binomial distribution functions:
+      template <class RealType, class Policy>
+      inline bool check_successes(const char* function, const RealType& r, RealType* result, const Policy& pol)
+      {
+        if( !(boost::math::isfinite)(r) || (r <= 0) )
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "Number of successes argument is %1%, but must be > 0 !", r, pol);
+          return false;
+        }
+        return true;
+      }
+      template <class RealType, class Policy>
+      inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol)
+      {
+        if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) )
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol);
+          return false;
+        }
+        return true;
+      }
+      template <class RealType, class Policy>
+      inline bool check_dist(const char* function, const RealType& r, const RealType& p, RealType* result, const Policy& pol)
+      {
+        return check_success_fraction(function, p, result, pol)
+          && check_successes(function, r, result, pol);
+      }
+      template <class RealType, class Policy>
+      inline bool check_dist_and_k(const char* function, const RealType& r, const RealType& p, RealType k, RealType* result, const Policy& pol)
+      {
+        if(check_dist(function, r, p, result, pol) == false)
+        {
+          return false;
+        }
+        if( !(boost::math::isfinite)(k) || (k < 0) )
+        { // Check k failures.
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "Number of failures argument is %1%, but must be >= 0 !", k, pol);
+          return false;
+        }
+        return true;
+      } // Check_dist_and_k
+
+      template <class RealType, class Policy>
+      inline bool check_dist_and_prob(const char* function, const RealType& r, RealType p, RealType prob, RealType* result, const Policy& pol)
+      {
+        if((check_dist(function, r, p, result, pol) && detail::check_probability(function, prob, result, pol)) == false)
+        {
+          return false;
+        }
+        return true;
+      } // check_dist_and_prob
+    } //  namespace negative_binomial_detail
+
+    template <class RealType = double, class Policy = policies::policy<> >
+    class negative_binomial_distribution
+    {
+    public:
+      typedef RealType value_type;
+      typedef Policy policy_type;
+
+      negative_binomial_distribution(RealType r, RealType p) : m_r(r), m_p(p)
+      { // Constructor.
+        RealType result;
+        negative_binomial_detail::check_dist(
+          "negative_binomial_distribution<%1%>::negative_binomial_distribution",
+          m_r, // Check successes r > 0.
+          m_p, // Check success_fraction 0 <= p <= 1.
+          &result, Policy());
+      } // negative_binomial_distribution constructor.
+
+      // Private data getter class member functions.
+      RealType success_fraction() const
+      { // Probability of success as fraction in range 0 to 1.
+        return m_p;
+      }
+      RealType successes() const
+      { // Total number of successes r.
+        return m_r;
+      }
+
+      static RealType find_lower_bound_on_p(
+        RealType trials,
+        RealType successes,
+        RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
+      {
+        static const char* function = "boost::math::negative_binomial<%1%>::find_lower_bound_on_p";
+        RealType result = 0;  // of error checks.
+        RealType failures = trials - successes;
+        if(false == detail::check_probability(function, alpha, &result, Policy())
+          && negative_binomial_detail::check_dist_and_k(
+          function, successes, RealType(0), failures, &result, Policy()))
+        {
+          return result;
+        }
+        // Use complement ibeta_inv function for lower bound.
+        // This is adapted from the corresponding binomial formula
+        // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
+        // This is a Clopper-Pearson interval, and may be overly conservative,
+        // see also "A Simple Improved Inferential Method for Some
+        // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY
+        // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
+        //
+        return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy());
+      } // find_lower_bound_on_p
+
+      static RealType find_upper_bound_on_p(
+        RealType trials,
+        RealType successes,
+        RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
+      {
+        static const char* function = "boost::math::negative_binomial<%1%>::find_upper_bound_on_p";
+        RealType result = 0;  // of error checks.
+        RealType failures = trials - successes;
+        if(false == negative_binomial_detail::check_dist_and_k(
+          function, successes, RealType(0), failures, &result, Policy())
+          && detail::check_probability(function, alpha, &result, Policy()))
+        {
+          return result;
+        }
+        if(failures == 0)
+           return 1;
+        // Use complement ibetac_inv function for upper bound.
+        // Note adjusted failures value: *not* failures+1 as usual.
+        // This is adapted from the corresponding binomial formula
+        // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
+        // This is a Clopper-Pearson interval, and may be overly conservative,
+        // see also "A Simple Improved Inferential Method for Some
+        // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY
+        // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
+        //
+        return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy());
+      } // find_upper_bound_on_p
+
+      // Estimate number of trials :
+      // "How many trials do I need to be P% sure of seeing k or fewer failures?"
+
+      static RealType find_minimum_number_of_trials(
+        RealType k,     // number of failures (k >= 0).
+        RealType p,     // success fraction 0 <= p <= 1.
+        RealType alpha) // risk level threshold 0 <= alpha <= 1.
+      {
+        static const char* function = "boost::math::negative_binomial<%1%>::find_minimum_number_of_trials";
+        // Error checks:
+        RealType result = 0;
+        if(false == negative_binomial_detail::check_dist_and_k(
+          function, RealType(1), p, k, &result, Policy())
+          && detail::check_probability(function, alpha, &result, Policy()))
+        { return result; }
+
+        result = ibeta_inva(k + 1, p, alpha, Policy());  // returns n - k
+        return result + k;
+      } // RealType find_number_of_failures
+
+      static RealType find_maximum_number_of_trials(
+        RealType k,     // number of failures (k >= 0).
+        RealType p,     // success fraction 0 <= p <= 1.
+        RealType alpha) // risk level threshold 0 <= alpha <= 1.
+      {
+        static const char* function = "boost::math::negative_binomial<%1%>::find_maximum_number_of_trials";
+        // Error checks:
+        RealType result = 0;
+        if(false == negative_binomial_detail::check_dist_and_k(
+          function, RealType(1), p, k, &result, Policy())
+          &&  detail::check_probability(function, alpha, &result, Policy()))
+        { return result; }
+
+        result = ibetac_inva(k + 1, p, alpha, Policy());  // returns n - k
+        return result + k;
+      } // RealType find_number_of_trials complemented
+
+    private:
+      RealType m_r; // successes.
+      RealType m_p; // success_fraction
+    }; // template <class RealType, class Policy> class negative_binomial_distribution
+
+    typedef negative_binomial_distribution<double> negative_binomial; // Reserved name of type double.
+
+    template <class RealType, class Policy>
+    inline const std::pair<RealType, RealType> range(const negative_binomial_distribution<RealType, Policy>& /* dist */)
+    { // Range of permissible values for random variable k.
+       using boost::math::tools::max_value;
+       return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer?
+    }
+
+    template <class RealType, class Policy>
+    inline const std::pair<RealType, RealType> support(const negative_binomial_distribution<RealType, Policy>& /* dist */)
+    { // Range of supported values for random variable k.
+       // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
+       using boost::math::tools::max_value;
+       return std::pair<RealType, RealType>(static_cast<RealType>(0),  max_value<RealType>()); // max_integer?
+    }
+
+    template <class RealType, class Policy>
+    inline RealType mean(const negative_binomial_distribution<RealType, Policy>& dist)
+    { // Mean of Negative Binomial distribution = r(1-p)/p.
+      return dist.successes() * (1 - dist.success_fraction() ) / dist.success_fraction();
+    } // mean
+
+    //template <class RealType, class Policy>
+    //inline RealType median(const negative_binomial_distribution<RealType, Policy>& dist)
+    //{ // Median of negative_binomial_distribution is not defined.
+    //  return policies::raise_domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN());
+    //} // median
+    // Now implemented via quantile(half) in derived accessors.
+
+    template <class RealType, class Policy>
+    inline RealType mode(const negative_binomial_distribution<RealType, Policy>& dist)
+    { // Mode of Negative Binomial distribution = floor[(r-1) * (1 - p)/p]
+      BOOST_MATH_STD_USING // ADL of std functions.
+      return floor((dist.successes() -1) * (1 - dist.success_fraction()) / dist.success_fraction());
+    } // mode
+
+    template <class RealType, class Policy>
+    inline RealType skewness(const negative_binomial_distribution<RealType, Policy>& dist)
+    { // skewness of Negative Binomial distribution = 2-p / (sqrt(r(1-p))
+      BOOST_MATH_STD_USING // ADL of std functions.
+      RealType p = dist.success_fraction();
+      RealType r = dist.successes();
+
+      return (2 - p) /
+        sqrt(r * (1 - p));
+    } // skewness
+
+    template <class RealType, class Policy>
+    inline RealType kurtosis(const negative_binomial_distribution<RealType, Policy>& dist)
+    { // kurtosis of Negative Binomial distribution
+      // http://en.wikipedia.org/wiki/Negative_binomial is kurtosis_excess so add 3
+      RealType p = dist.success_fraction();
+      RealType r = dist.successes();
+      return 3 + (6 / r) + ((p * p) / (r * (1 - p)));
+    } // kurtosis
+
+     template <class RealType, class Policy>
+    inline RealType kurtosis_excess(const negative_binomial_distribution<RealType, Policy>& dist)
+    { // kurtosis excess of Negative Binomial distribution
+      // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess
+      RealType p = dist.success_fraction();
+      RealType r = dist.successes();
+      return (6 - p * (6-p)) / (r * (1-p));
+    } // kurtosis_excess
+
+    template <class RealType, class Policy>
+    inline RealType variance(const negative_binomial_distribution<RealType, Policy>& dist)
+    { // Variance of Binomial distribution = r (1-p) / p^2.
+      return  dist.successes() * (1 - dist.success_fraction())
+        / (dist.success_fraction() * dist.success_fraction());
+    } // variance
+
+    // RealType standard_deviation(const negative_binomial_distribution<RealType, Policy>& dist)
+    // standard_deviation provided by derived accessors.
+    // RealType hazard(const negative_binomial_distribution<RealType, Policy>& dist)
+    // hazard of Negative Binomial distribution provided by derived accessors.
+    // RealType chf(const negative_binomial_distribution<RealType, Policy>& dist)
+    // chf of Negative Binomial distribution provided by derived accessors.
+
+    template <class RealType, class Policy>
+    inline RealType pdf(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& k)
+    { // Probability Density/Mass Function.
+      BOOST_FPU_EXCEPTION_GUARD
+
+      static const char* function = "boost::math::pdf(const negative_binomial_distribution<%1%>&, %1%)";
+
+      RealType r = dist.successes();
+      RealType p = dist.success_fraction();
+      RealType result = 0;
+      if(false == negative_binomial_detail::check_dist_and_k(
+        function,
+        r,
+        dist.success_fraction(),
+        k,
+        &result, Policy()))
+      {
+        return result;
+      }
+
+      result = (p/(r + k)) * ibeta_derivative(r, static_cast<RealType>(k+1), p, Policy());
+      // Equivalent to:
+      // return exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p, r) * pow((1-p), k);
+      return result;
+    } // negative_binomial_pdf
+
+    template <class RealType, class Policy>
+    inline RealType cdf(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& k)
+    { // Cumulative Distribution Function of Negative Binomial.
+      static const char* function = "boost::math::cdf(const negative_binomial_distribution<%1%>&, %1%)";
+      using boost::math::ibeta; // Regularized incomplete beta function.
+      // k argument may be integral, signed, or unsigned, or floating point.
+      // If necessary, it has already been promoted from an integral type.
+      RealType p = dist.success_fraction();
+      RealType r = dist.successes();
+      // Error check:
+      RealType result = 0;
+      if(false == negative_binomial_detail::check_dist_and_k(
+        function,
+        r,
+        dist.success_fraction(),
+        k,
+        &result, Policy()))
+      {
+        return result;
+      }
+
+      RealType probability = ibeta(r, static_cast<RealType>(k+1), p, Policy());
+      // Ip(r, k+1) = ibeta(r, k+1, p)
+      return probability;
+    } // cdf Cumulative Distribution Function Negative Binomial.
+
+      template <class RealType, class Policy>
+      inline RealType cdf(const complemented2_type<negative_binomial_distribution<RealType, Policy>, RealType>& c)
+      { // Complemented Cumulative Distribution Function Negative Binomial.
+
+      static const char* function = "boost::math::cdf(const negative_binomial_distribution<%1%>&, %1%)";
+      using boost::math::ibetac; // Regularized incomplete beta function complement.
+      // k argument may be integral, signed, or unsigned, or floating point.
+      // If necessary, it has already been promoted from an integral type.
+      RealType const& k = c.param;
+      negative_binomial_distribution<RealType, Policy> const& dist = c.dist;
+      RealType p = dist.success_fraction();
+      RealType r = dist.successes();
+      // Error check:
+      RealType result = 0;
+      if(false == negative_binomial_detail::check_dist_and_k(
+        function,
+        r,
+        p,
+        k,
+        &result, Policy()))
+      {
+        return result;
+      }
+      // Calculate cdf negative binomial using the incomplete beta function.
+      // Use of ibeta here prevents cancellation errors in calculating
+      // 1-p if p is very small, perhaps smaller than machine epsilon.
+      // Ip(k+1, r) = ibetac(r, k+1, p)
+      // constrain_probability here?
+     RealType probability = ibetac(r, static_cast<RealType>(k+1), p, Policy());
+      // Numerical errors might cause probability to be slightly outside the range < 0 or > 1.
+      // This might cause trouble downstream, so warn, possibly throw exception, but constrain to the limits.
+      return probability;
+    } // cdf Cumulative Distribution Function Negative Binomial.
+
+    template <class RealType, class Policy>
+    inline RealType quantile(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& P)
+    { // Quantile, percentile/100 or Percent Point Negative Binomial function.
+      // Return the number of expected failures k for a given probability p.
+
+      // Inverse cumulative Distribution Function or Quantile (percentile / 100) of negative_binomial Probability.
+      // MAthCAD pnbinom return smallest k such that negative_binomial(k, n, p) >= probability.
+      // k argument may be integral, signed, or unsigned, or floating point.
+      // BUT Cephes/CodeCogs says: finds argument p (0 to 1) such that cdf(k, n, p) = y
+      static const char* function = "boost::math::quantile(const negative_binomial_distribution<%1%>&, %1%)";
+      BOOST_MATH_STD_USING // ADL of std functions.
+
+      RealType p = dist.success_fraction();
+      RealType r = dist.successes();
+      // Check dist and P.
+      RealType result = 0;
+      if(false == negative_binomial_detail::check_dist_and_prob
+        (function, r, p, P, &result, Policy()))
+      {
+        return result;
+      }
+
+      // Special cases.
+      if (P == 1)
+      {  // Would need +infinity failures for total confidence.
+        result = policies::raise_overflow_error<RealType>(
+            function,
+            "Probability argument is 1, which implies infinite failures !", Policy());
+        return result;
+       // usually means return +std::numeric_limits<RealType>::infinity();
+       // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
+      }
+      if (P == 0)
+      { // No failures are expected if P = 0.
+        return 0; // Total trials will be just dist.successes.
+      }
+      if (P <= pow(dist.success_fraction(), dist.successes()))
+      { // p <= pdf(dist, 0) == cdf(dist, 0)
+        return 0;
+      }
+      if(p == 0)
+      {  // Would need +infinity failures for total confidence.
+         result = policies::raise_overflow_error<RealType>(
+            function,
+            "Success fraction is 0, which implies infinite failures !", Policy());
+         return result;
+         // usually means return +std::numeric_limits<RealType>::infinity();
+         // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
+      }
+      /*
+      // Calculate quantile of negative_binomial using the inverse incomplete beta function.
+      using boost::math::ibeta_invb;
+      return ibeta_invb(r, p, P, Policy()) - 1; //
+      */
+      RealType guess = 0;
+      RealType factor = 5;
+      if(r * r * r * P * p > 0.005)
+         guess = detail::inverse_negative_binomial_cornish_fisher(r, p, RealType(1-p), P, RealType(1-P), Policy());
+
+      if(guess < 10)
+      {
+         //
+         // Cornish-Fisher Negative binomial approximation not accurate in this area:
+         //
+         guess = (std::min)(RealType(r * 2), RealType(10));
+      }
+      else
+         factor = (1-P < sqrt(tools::epsilon<RealType>())) ? 2 : (guess < 20 ? 1.2f : 1.1f);
+      BOOST_MATH_INSTRUMENT_CODE("guess = " << guess);
+      //
+      // Max iterations permitted:
+      //
+      boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
+      typedef typename Policy::discrete_quantile_type discrete_type;
+      return detail::inverse_discrete_quantile(
+         dist,
+         P,
+         false,
+         guess,
+         factor,
+         RealType(1),
+         discrete_type(),
+         max_iter);
+    } // RealType quantile(const negative_binomial_distribution dist, p)
+
+    template <class RealType, class Policy>
+    inline RealType quantile(const complemented2_type<negative_binomial_distribution<RealType, Policy>, RealType>& c)
+    {  // Quantile or Percent Point Binomial function.
+       // Return the number of expected failures k for a given
+       // complement of the probability Q = 1 - P.
+       static const char* function = "boost::math::quantile(const negative_binomial_distribution<%1%>&, %1%)";
+       BOOST_MATH_STD_USING
+
+       // Error checks:
+       RealType Q = c.param;
+       const negative_binomial_distribution<RealType, Policy>& dist = c.dist;
+       RealType p = dist.success_fraction();
+       RealType r = dist.successes();
+       RealType result = 0;
+       if(false == negative_binomial_detail::check_dist_and_prob(
+          function,
+          r,
+          p,
+          Q,
+          &result, Policy()))
+       {
+          return result;
+       }
+
+       // Special cases:
+       //
+       if(Q == 1)
+       {  // There may actually be no answer to this question,
+          // since the probability of zero failures may be non-zero,
+          return 0; // but zero is the best we can do:
+       }
+       if(Q == 0)
+       {  // Probability 1 - Q  == 1 so infinite failures to achieve certainty.
+          // Would need +infinity failures for total confidence.
+          result = policies::raise_overflow_error<RealType>(
+             function,
+             "Probability argument complement is 0, which implies infinite failures !", Policy());
+          return result;
+          // usually means return +std::numeric_limits<RealType>::infinity();
+          // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
+       }
+       if (-Q <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy()))
+       {  // q <= cdf(complement(dist, 0)) == pdf(dist, 0)
+          return 0; //
+       }
+       if(p == 0)
+       {  // Success fraction is 0 so infinite failures to achieve certainty.
+          // Would need +infinity failures for total confidence.
+          result = policies::raise_overflow_error<RealType>(
+             function,
+             "Success fraction is 0, which implies infinite failures !", Policy());
+          return result;
+          // usually means return +std::numeric_limits<RealType>::infinity();
+          // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
+       }
+       //return ibetac_invb(r, p, Q, Policy()) -1;
+       RealType guess = 0;
+       RealType factor = 5;
+       if(r * r * r * (1-Q) * p > 0.005)
+          guess = detail::inverse_negative_binomial_cornish_fisher(r, p, RealType(1-p), RealType(1-Q), Q, Policy());
+
+       if(guess < 10)
+       {
+          //
+          // Cornish-Fisher Negative binomial approximation not accurate in this area:
+          //
+          guess = (std::min)(RealType(r * 2), RealType(10));
+       }
+       else
+          factor = (Q < sqrt(tools::epsilon<RealType>())) ? 2 : (guess < 20 ? 1.2f : 1.1f);
+       BOOST_MATH_INSTRUMENT_CODE("guess = " << guess);
+       //
+       // Max iterations permitted:
+       //
+       boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
+       typedef typename Policy::discrete_quantile_type discrete_type;
+       return detail::inverse_discrete_quantile(
+          dist,
+          Q,
+          true,
+          guess,
+          factor,
+          RealType(1),
+          discrete_type(),
+          max_iter);
+    } // quantile complement
+
+ } // namespace math
+} // namespace boost
+
+// This include must be at the end, *after* the accessors
+// for this distribution have been defined, in order to
+// keep compilers that support two-phase lookup happy.
+#include <boost/math/distributions/detail/derived_accessors.hpp>
+
+#if defined (BOOST_MSVC)
+# pragma warning(pop)
+#endif
+
+#endif // BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP