Chris@16: // boost\math\distributions\geometric.hpp
Chris@16: 
Chris@16: // Copyright John Maddock 2010.
Chris@16: // Copyright Paul A. Bristow 2010.
Chris@16: 
Chris@16: // Use, modification and distribution are subject to the
Chris@16: // Boost Software License, Version 1.0.
Chris@16: // (See accompanying file LICENSE_1_0.txt
Chris@16: // or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: // geometric distribution is a discrete probability distribution.
Chris@16: // It expresses the probability distribution of the number (k) of
Chris@16: // events, occurrences, failures or arrivals before the first success.
Chris@16: // supported on the set {0, 1, 2, 3...}
Chris@16: 
Chris@16: // Note that the set includes zero (unlike some definitions that start at one).
Chris@16: 
Chris@16: // The random variate k is the number of events, occurrences or arrivals.
Chris@16: // k argument may be integral, signed, or unsigned, or floating point.
Chris@16: // If necessary, it has already been promoted from an integral type.
Chris@16: 
Chris@16: // Note that the geometric distribution
Chris@16: // (like others including the binomial, geometric & Bernoulli)
Chris@16: // is strictly defined as a discrete function:
Chris@16: // only integral values of k are envisaged.
Chris@16: // However because the method of calculation uses a continuous gamma function,
Chris@16: // it is convenient to treat it as if a continous function,
Chris@16: // and permit non-integral values of k.
Chris@16: // To enforce the strict mathematical model, users should use floor or ceil functions
Chris@16: // on k outside this function to ensure that k is integral.
Chris@16: 
Chris@16: // See http://en.wikipedia.org/wiki/geometric_distribution
Chris@16: // http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html
Chris@16: // http://mathworld.wolfram.com/GeometricDistribution.html
Chris@16: 
Chris@16: #ifndef BOOST_MATH_SPECIAL_GEOMETRIC_HPP
Chris@16: #define BOOST_MATH_SPECIAL_GEOMETRIC_HPP
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b).
Chris@16: #include <boost/math/distributions/complement.hpp> // complement.
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error.
Chris@16: #include <boost/math/special_functions/fpclassify.hpp> // isnan.
Chris@16: #include <boost/math/tools/roots.hpp> // for root finding.
Chris@16: #include <boost/math/distributions/detail/inv_discrete_quantile.hpp>
Chris@16: 
Chris@16: #include <boost/type_traits/is_floating_point.hpp>
Chris@16: #include <boost/type_traits/is_integral.hpp>
Chris@16: #include <boost/type_traits/is_same.hpp>
Chris@16: #include <boost/mpl/if.hpp>
Chris@16: 
Chris@16: #include <limits> // using std::numeric_limits;
Chris@16: #include <utility>
Chris@16: 
Chris@16: #if defined (BOOST_MSVC)
Chris@16: #  pragma warning(push)
Chris@16: // This believed not now necessary, so commented out.
Chris@16: //#  pragma warning(disable: 4702) // unreachable code.
Chris@16: // in domain_error_imp in error_handling.
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost
Chris@16: {
Chris@16:   namespace math
Chris@16:   {
Chris@16:     namespace geometric_detail
Chris@16:     {
Chris@16:       // Common error checking routines for geometric distribution function:
Chris@16:       template <class RealType, class Policy>
Chris@16:       inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol)
Chris@16:       {
Chris@16:         if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) )
Chris@16:         {
Chris@16:           *result = policies::raise_domain_error<RealType>(
Chris@16:             function,
Chris@16:             "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol);
Chris@16:           return false;
Chris@16:         }
Chris@16:         return true;
Chris@16:       }
Chris@16: 
Chris@16:       template <class RealType, class Policy>
Chris@16:       inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& pol)
Chris@16:       {
Chris@16:         return check_success_fraction(function, p, result, pol);
Chris@16:       }
Chris@16: 
Chris@16:       template <class RealType, class Policy>
Chris@16:       inline bool check_dist_and_k(const char* function,  const RealType& p, RealType k, RealType* result, const Policy& pol)
Chris@16:       {
Chris@16:         if(check_dist(function, p, result, pol) == false)
Chris@16:         {
Chris@16:           return false;
Chris@16:         }
Chris@16:         if( !(boost::math::isfinite)(k) || (k < 0) )
Chris@16:         { // Check k failures.
Chris@16:           *result = policies::raise_domain_error<RealType>(
Chris@16:             function,
Chris@16:             "Number of failures argument is %1%, but must be >= 0 !", k, pol);
Chris@16:           return false;
Chris@16:         }
Chris@16:         return true;
Chris@16:       } // Check_dist_and_k
Chris@16: 
Chris@16:       template <class RealType, class Policy>
Chris@16:       inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& pol)
Chris@16:       {
Chris@16:         if(check_dist(function, p, result, pol) && detail::check_probability(function, prob, result, pol) == false)
Chris@16:         {
Chris@16:           return false;
Chris@16:         }
Chris@16:         return true;
Chris@16:       } // check_dist_and_prob
Chris@16:     } //  namespace geometric_detail
Chris@16: 
Chris@16:     template <class RealType = double, class Policy = policies::policy<> >
Chris@16:     class geometric_distribution
Chris@16:     {
Chris@16:     public:
Chris@16:       typedef RealType value_type;
Chris@16:       typedef Policy policy_type;
Chris@16: 
Chris@16:       geometric_distribution(RealType p) : m_p(p)
Chris@16:       { // Constructor stores success_fraction p.
Chris@16:         RealType result;
Chris@16:         geometric_detail::check_dist(
Chris@16:           "geometric_distribution<%1%>::geometric_distribution",
Chris@16:           m_p, // Check success_fraction 0 <= p <= 1.
Chris@16:           &result, Policy());
Chris@16:       } // geometric_distribution constructor.
Chris@16: 
Chris@16:       // Private data getter class member functions.
Chris@16:       RealType success_fraction() const
Chris@16:       { // Probability of success as fraction in range 0 to 1.
Chris@16:         return m_p;
Chris@16:       }
Chris@16:       RealType successes() const
Chris@16:       { // Total number of successes r = 1 (for compatibility with negative binomial?).
Chris@16:         return 1;
Chris@16:       }
Chris@16: 
Chris@16:       // Parameter estimation.
Chris@16:       // (These are copies of negative_binomial distribution with successes = 1).
Chris@16:       static RealType find_lower_bound_on_p(
Chris@16:         RealType trials,
Chris@16:         RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
Chris@16:       {
Chris@16:         static const char* function = "boost::math::geometric<%1%>::find_lower_bound_on_p";
Chris@16:         RealType result = 0;  // of error checks.
Chris@16:         RealType successes = 1;
Chris@16:         RealType failures = trials - successes;
Chris@16:         if(false == detail::check_probability(function, alpha, &result, Policy())
Chris@16:           && geometric_detail::check_dist_and_k(
Chris@16:           function, RealType(0), failures, &result, Policy()))
Chris@16:         {
Chris@16:           return result;
Chris@16:         }
Chris@16:         // Use complement ibeta_inv function for lower bound.
Chris@16:         // This is adapted from the corresponding binomial formula
Chris@16:         // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
Chris@16:         // This is a Clopper-Pearson interval, and may be overly conservative,
Chris@16:         // see also "A Simple Improved Inferential Method for Some
Chris@16:         // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY
Chris@16:         // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
Chris@16:         //
Chris@16:         return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy());
Chris@16:       } // find_lower_bound_on_p
Chris@16: 
Chris@16:       static RealType find_upper_bound_on_p(
Chris@16:         RealType trials,
Chris@16:         RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
Chris@16:       {
Chris@16:         static const char* function = "boost::math::geometric<%1%>::find_upper_bound_on_p";
Chris@16:         RealType result = 0;  // of error checks.
Chris@16:         RealType successes = 1;
Chris@16:         RealType failures = trials - successes;
Chris@16:         if(false == geometric_detail::check_dist_and_k(
Chris@16:           function, RealType(0), failures, &result, Policy())
Chris@16:           && detail::check_probability(function, alpha, &result, Policy()))
Chris@16:         {
Chris@16:           return result;
Chris@16:         }
Chris@16:         if(failures == 0)
Chris@16:         {
Chris@16:            return 1;
Chris@16:         }// Use complement ibetac_inv function for upper bound.
Chris@16:         // Note adjusted failures value: *not* failures+1 as usual.
Chris@16:         // This is adapted from the corresponding binomial formula
Chris@16:         // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
Chris@16:         // This is a Clopper-Pearson interval, and may be overly conservative,
Chris@16:         // see also "A Simple Improved Inferential Method for Some
Chris@16:         // Discrete Distributions" Yong CAI and K. Krishnamoorthy
Chris@16:         // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
Chris@16:         //
Chris@16:         return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy());
Chris@16:       } // find_upper_bound_on_p
Chris@16: 
Chris@16:       // Estimate number of trials :
Chris@16:       // "How many trials do I need to be P% sure of seeing k or fewer failures?"
Chris@16: 
Chris@16:       static RealType find_minimum_number_of_trials(
Chris@16:         RealType k,     // number of failures (k >= 0).
Chris@16:         RealType p,     // success fraction 0 <= p <= 1.
Chris@16:         RealType alpha) // risk level threshold 0 <= alpha <= 1.
Chris@16:       {
Chris@16:         static const char* function = "boost::math::geometric<%1%>::find_minimum_number_of_trials";
Chris@16:         // Error checks:
Chris@16:         RealType result = 0;
Chris@16:         if(false == geometric_detail::check_dist_and_k(
Chris@16:           function, p, k, &result, Policy())
Chris@16:           && detail::check_probability(function, alpha, &result, Policy()))
Chris@16:         {
Chris@16:           return result;
Chris@16:         }
Chris@16:         result = ibeta_inva(k + 1, p, alpha, Policy());  // returns n - k
Chris@16:         return result + k;
Chris@16:       } // RealType find_number_of_failures
Chris@16: 
Chris@16:       static RealType find_maximum_number_of_trials(
Chris@16:         RealType k,     // number of failures (k >= 0).
Chris@16:         RealType p,     // success fraction 0 <= p <= 1.
Chris@16:         RealType alpha) // risk level threshold 0 <= alpha <= 1.
Chris@16:       {
Chris@16:         static const char* function = "boost::math::geometric<%1%>::find_maximum_number_of_trials";
Chris@16:         // Error checks:
Chris@16:         RealType result = 0;
Chris@16:         if(false == geometric_detail::check_dist_and_k(
Chris@16:           function, p, k, &result, Policy())
Chris@16:           &&  detail::check_probability(function, alpha, &result, Policy()))
Chris@16:         { 
Chris@16:           return result;
Chris@16:         }
Chris@16:         result = ibetac_inva(k + 1, p, alpha, Policy());  // returns n - k
Chris@16:         return result + k;
Chris@16:       } // RealType find_number_of_trials complemented
Chris@16: 
Chris@16:     private:
Chris@16:       //RealType m_r; // successes fixed at unity.
Chris@16:       RealType m_p; // success_fraction
Chris@16:     }; // template <class RealType, class Policy> class geometric_distribution
Chris@16: 
Chris@16:     typedef geometric_distribution<double> geometric; // Reserved name of type double.
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline const std::pair<RealType, RealType> range(const geometric_distribution<RealType, Policy>& /* dist */)
Chris@16:     { // Range of permissible values for random variable k.
Chris@16:        using boost::math::tools::max_value;
Chris@16:        return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer?
Chris@16:     }
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline const std::pair<RealType, RealType> support(const geometric_distribution<RealType, Policy>& /* dist */)
Chris@16:     { // Range of supported values for random variable k.
Chris@16:        // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@16:        using boost::math::tools::max_value;
Chris@16:        return std::pair<RealType, RealType>(static_cast<RealType>(0),  max_value<RealType>()); // max_integer?
Chris@16:     }
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType mean(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     { // Mean of geometric distribution = (1-p)/p.
Chris@16:       return (1 - dist.success_fraction() ) / dist.success_fraction();
Chris@16:     } // mean
Chris@16: 
Chris@16:     // median implemented via quantile(half) in derived accessors.
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType mode(const geometric_distribution<RealType, Policy>&)
Chris@16:     { // Mode of geometric distribution = zero.
Chris@16:       BOOST_MATH_STD_USING // ADL of std functions.
Chris@16:       return 0;
Chris@16:     } // mode
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType variance(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     { // Variance of Binomial distribution = (1-p) / p^2.
Chris@16:       return  (1 - dist.success_fraction())
Chris@16:         / (dist.success_fraction() * dist.success_fraction());
Chris@16:     } // variance
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType skewness(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     { // skewness of geometric distribution = 2-p / (sqrt(r(1-p))
Chris@16:       BOOST_MATH_STD_USING // ADL of std functions.
Chris@16:       RealType p = dist.success_fraction();
Chris@16:       return (2 - p) / sqrt(1 - p);
Chris@16:     } // skewness
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType kurtosis(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     { // kurtosis of geometric distribution
Chris@16:       // http://en.wikipedia.org/wiki/geometric is kurtosis_excess so add 3
Chris@16:       RealType p = dist.success_fraction();
Chris@16:       return 3 + (p*p - 6*p + 6) / (1 - p);
Chris@16:     } // kurtosis
Chris@16: 
Chris@16:      template <class RealType, class Policy>
Chris@16:     inline RealType kurtosis_excess(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     { // kurtosis excess of geometric distribution
Chris@16:       // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess
Chris@16:       RealType p = dist.success_fraction();
Chris@16:       return (p*p - 6*p + 6) / (1 - p);
Chris@16:     } // kurtosis_excess
Chris@16: 
Chris@16:     // RealType standard_deviation(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     // standard_deviation provided by derived accessors.
Chris@16:     // RealType hazard(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     // hazard of geometric distribution provided by derived accessors.
Chris@16:     // RealType chf(const geometric_distribution<RealType, Policy>& dist)
Chris@16:     // chf of geometric distribution provided by derived accessors.
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType pdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
Chris@16:     { // Probability Density/Mass Function.
Chris@16:       BOOST_FPU_EXCEPTION_GUARD
Chris@16:       BOOST_MATH_STD_USING  // For ADL of math functions.
Chris@16:       static const char* function = "boost::math::pdf(const geometric_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:       RealType p = dist.success_fraction();
Chris@16:       RealType result = 0;
Chris@16:       if(false == geometric_detail::check_dist_and_k(
Chris@16:         function,
Chris@16:         p,
Chris@16:         k,
Chris@16:         &result, Policy()))
Chris@16:       {
Chris@16:         return result;
Chris@16:       }
Chris@16:       if (k == 0)
Chris@16:       {
Chris@16:         return p; // success_fraction
Chris@16:       }
Chris@16:       RealType q = 1 - p;  // Inaccurate for small p?
Chris@16:       // So try to avoid inaccuracy for large or small p.
Chris@16:       // but has little effect > last significant bit.
Chris@16:       //cout << "p *  pow(q, k) " << result << endl; // seems best whatever p
Chris@16:       //cout << "exp(p * k * log1p(-p)) " << p * exp(k * log1p(-p)) << endl;
Chris@16:       //if (p < 0.5)
Chris@16:       //{
Chris@16:       //  result = p *  pow(q, k);
Chris@16:       //}
Chris@16:       //else
Chris@16:       //{
Chris@16:       //  result = p * exp(k * log1p(-p));
Chris@16:       //}
Chris@16:       result = p * pow(q, k);
Chris@16:       return result;
Chris@16:     } // geometric_pdf
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType cdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
Chris@16:     { // Cumulative Distribution Function of geometric.
Chris@16:       static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:       // k argument may be integral, signed, or unsigned, or floating point.
Chris@16:       // If necessary, it has already been promoted from an integral type.
Chris@16:       RealType p = dist.success_fraction();
Chris@16:       // Error check:
Chris@16:       RealType result = 0;
Chris@16:       if(false == geometric_detail::check_dist_and_k(
Chris@16:         function,
Chris@16:         p,
Chris@16:         k,
Chris@16:         &result, Policy()))
Chris@16:       {
Chris@16:         return result;
Chris@16:       }
Chris@16:       if(k == 0)
Chris@16:       {
Chris@16:         return p; // success_fraction
Chris@16:       }
Chris@16:       //RealType q = 1 - p;  // Bad for small p
Chris@16:       //RealType probability = 1 - std::pow(q, k+1);
Chris@16: 
Chris@101:       RealType z = boost::math::log1p(-p, Policy()) * (k + 1);
Chris@101:       RealType probability = -boost::math::expm1(z, Policy());
Chris@16: 
Chris@16:       return probability;
Chris@16:     } // cdf Cumulative Distribution Function geometric.
Chris@16: 
Chris@16:       template <class RealType, class Policy>
Chris@16:       inline RealType cdf(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c)
Chris@16:       { // Complemented Cumulative Distribution Function geometric.
Chris@16:       BOOST_MATH_STD_USING
Chris@16:       static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
Chris@16:       // k argument may be integral, signed, or unsigned, or floating point.
Chris@16:       // If necessary, it has already been promoted from an integral type.
Chris@16:       RealType const& k = c.param;
Chris@16:       geometric_distribution<RealType, Policy> const& dist = c.dist;
Chris@16:       RealType p = dist.success_fraction();
Chris@16:       // Error check:
Chris@16:       RealType result = 0;
Chris@16:       if(false == geometric_detail::check_dist_and_k(
Chris@16:         function,
Chris@16:         p,
Chris@16:         k,
Chris@16:         &result, Policy()))
Chris@16:       {
Chris@16:         return result;
Chris@16:       }
Chris@101:       RealType z = boost::math::log1p(-p, Policy()) * (k+1);
Chris@16:       RealType probability = exp(z);
Chris@16:       return probability;
Chris@16:     } // cdf Complemented Cumulative Distribution Function geometric.
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType quantile(const geometric_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16:     { // Quantile, percentile/100 or Percent Point geometric function.
Chris@16:       // Return the number of expected failures k for a given probability p.
Chris@16: 
Chris@16:       // Inverse cumulative Distribution Function or Quantile (percentile / 100) of geometric Probability.
Chris@16:       // k argument may be integral, signed, or unsigned, or floating point.
Chris@16: 
Chris@16:       static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)";
Chris@16:       BOOST_MATH_STD_USING // ADL of std functions.
Chris@16: 
Chris@16:       RealType success_fraction = dist.success_fraction();
Chris@16:       // Check dist and x.
Chris@16:       RealType result = 0;
Chris@16:       if(false == geometric_detail::check_dist_and_prob
Chris@16:         (function, success_fraction, x, &result, Policy()))
Chris@16:       {
Chris@16:         return result;
Chris@16:       }
Chris@16: 
Chris@16:       // Special cases.
Chris@16:       if (x == 1)
Chris@16:       {  // Would need +infinity failures for total confidence.
Chris@16:         result = policies::raise_overflow_error<RealType>(
Chris@16:             function,
Chris@16:             "Probability argument is 1, which implies infinite failures !", Policy());
Chris@16:         return result;
Chris@16:        // usually means return +std::numeric_limits<RealType>::infinity();
Chris@16:        // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
Chris@16:       }
Chris@16:       if (x == 0)
Chris@16:       { // No failures are expected if P = 0.
Chris@16:         return 0; // Total trials will be just dist.successes.
Chris@16:       }
Chris@16:       // if (P <= pow(dist.success_fraction(), 1))
Chris@16:       if (x <= success_fraction)
Chris@16:       { // p <= pdf(dist, 0) == cdf(dist, 0)
Chris@16:         return 0;
Chris@16:       }
Chris@16:       if (x == 1)
Chris@16:       {
Chris@16:         return 0;
Chris@16:       }
Chris@16:    
Chris@16:       // log(1-x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small
Chris@101:       result = boost::math::log1p(-x, Policy()) / boost::math::log1p(-success_fraction, Policy()) - 1;
Chris@16:       // Subtract a few epsilons here too?
Chris@16:       // to make sure it doesn't slip over, so ceil would be one too many.
Chris@16:       return result;
Chris@16:     } // RealType quantile(const geometric_distribution dist, p)
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType quantile(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c)
Chris@16:     {  // Quantile or Percent Point Binomial function.
Chris@16:        // Return the number of expected failures k for a given
Chris@16:        // complement of the probability Q = 1 - P.
Chris@16:        static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)";
Chris@16:        BOOST_MATH_STD_USING
Chris@16:        // Error checks:
Chris@16:        RealType x = c.param;
Chris@16:        const geometric_distribution<RealType, Policy>& dist = c.dist;
Chris@16:        RealType success_fraction = dist.success_fraction();
Chris@16:        RealType result = 0;
Chris@16:        if(false == geometric_detail::check_dist_and_prob(
Chris@16:           function,
Chris@16:           success_fraction,
Chris@16:           x,
Chris@16:           &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16: 
Chris@16:        // Special cases:
Chris@16:        if(x == 1)
Chris@16:        {  // There may actually be no answer to this question,
Chris@16:           // since the probability of zero failures may be non-zero,
Chris@16:           return 0; // but zero is the best we can do:
Chris@16:        }
Chris@16:        if (-x <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy()))
Chris@16:        {  // q <= cdf(complement(dist, 0)) == pdf(dist, 0)
Chris@16:           return 0; //
Chris@16:        }
Chris@16:        if(x == 0)
Chris@16:        {  // Probability 1 - Q  == 1 so infinite failures to achieve certainty.
Chris@16:           // Would need +infinity failures for total confidence.
Chris@16:           result = policies::raise_overflow_error<RealType>(
Chris@16:              function,
Chris@16:              "Probability argument complement is 0, which implies infinite failures !", Policy());
Chris@16:           return result;
Chris@16:           // usually means return +std::numeric_limits<RealType>::infinity();
Chris@16:           // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
Chris@16:        }
Chris@16:        // log(x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small
Chris@101:        result = log(x) / boost::math::log1p(-success_fraction, Policy()) - 1;
Chris@16:       return result;
Chris@16: 
Chris@16:     } // quantile complement
Chris@16: 
Chris@16:  } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: // This include must be at the end, *after* the accessors
Chris@16: // for this distribution have been defined, in order to
Chris@16: // keep compilers that support two-phase lookup happy.
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #if defined (BOOST_MSVC)
Chris@16: # pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: #endif // BOOST_MATH_SPECIAL_GEOMETRIC_HPP