cannam@160: // boost\math\distributions\geometric.hpp
cannam@160: 
cannam@160: // Copyright John Maddock 2010.
cannam@160: // Copyright Paul A. Bristow 2010.
cannam@160: 
cannam@160: // Use, modification and distribution are subject to the
cannam@160: // Boost Software License, Version 1.0.
cannam@160: // (See accompanying file LICENSE_1_0.txt
cannam@160: // or copy at http://www.boost.org/LICENSE_1_0.txt)
cannam@160: 
cannam@160: // geometric distribution is a discrete probability distribution.
cannam@160: // It expresses the probability distribution of the number (k) of
cannam@160: // events, occurrences, failures or arrivals before the first success.
cannam@160: // supported on the set {0, 1, 2, 3...}
cannam@160: 
cannam@160: // Note that the set includes zero (unlike some definitions that start at one).
cannam@160: 
cannam@160: // The random variate k is the number of events, occurrences or arrivals.
cannam@160: // k argument may be integral, signed, or unsigned, or floating point.
cannam@160: // If necessary, it has already been promoted from an integral type.
cannam@160: 
cannam@160: // Note that the geometric distribution
cannam@160: // (like others including the binomial, geometric & Bernoulli)
cannam@160: // is strictly defined as a discrete function:
cannam@160: // only integral values of k are envisaged.
cannam@160: // However because the method of calculation uses a continuous gamma function,
cannam@160: // it is convenient to treat it as if a continous function,
cannam@160: // and permit non-integral values of k.
cannam@160: // To enforce the strict mathematical model, users should use floor or ceil functions
cannam@160: // on k outside this function to ensure that k is integral.
cannam@160: 
cannam@160: // See http://en.wikipedia.org/wiki/geometric_distribution
cannam@160: // http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html
cannam@160: // http://mathworld.wolfram.com/GeometricDistribution.html
cannam@160: 
cannam@160: #ifndef BOOST_MATH_SPECIAL_GEOMETRIC_HPP
cannam@160: #define BOOST_MATH_SPECIAL_GEOMETRIC_HPP
cannam@160: 
cannam@160: #include <boost/math/distributions/fwd.hpp>
cannam@160: #include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b).
cannam@160: #include <boost/math/distributions/complement.hpp> // complement.
cannam@160: #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error.
cannam@160: #include <boost/math/special_functions/fpclassify.hpp> // isnan.
cannam@160: #include <boost/math/tools/roots.hpp> // for root finding.
cannam@160: #include <boost/math/distributions/detail/inv_discrete_quantile.hpp>
cannam@160: 
cannam@160: #include <boost/type_traits/is_floating_point.hpp>
cannam@160: #include <boost/type_traits/is_integral.hpp>
cannam@160: #include <boost/type_traits/is_same.hpp>
cannam@160: #include <boost/mpl/if.hpp>
cannam@160: 
cannam@160: #include <limits> // using std::numeric_limits;
cannam@160: #include <utility>
cannam@160: 
cannam@160: #if defined (BOOST_MSVC)
cannam@160: #  pragma warning(push)
cannam@160: // This believed not now necessary, so commented out.
cannam@160: //#  pragma warning(disable: 4702) // unreachable code.
cannam@160: // in domain_error_imp in error_handling.
cannam@160: #endif
cannam@160: 
cannam@160: namespace boost
cannam@160: {
cannam@160:   namespace math
cannam@160:   {
cannam@160:     namespace geometric_detail
cannam@160:     {
cannam@160:       // Common error checking routines for geometric distribution function:
cannam@160:       template <class RealType, class Policy>
cannam@160:       inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol)
cannam@160:       {
cannam@160:         if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) )
cannam@160:         {
cannam@160:           *result = policies::raise_domain_error<RealType>(
cannam@160:             function,
cannam@160:             "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol);
cannam@160:           return false;
cannam@160:         }
cannam@160:         return true;
cannam@160:       }
cannam@160: 
cannam@160:       template <class RealType, class Policy>
cannam@160:       inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& pol)
cannam@160:       {
cannam@160:         return check_success_fraction(function, p, result, pol);
cannam@160:       }
cannam@160: 
cannam@160:       template <class RealType, class Policy>
cannam@160:       inline bool check_dist_and_k(const char* function,  const RealType& p, RealType k, RealType* result, const Policy& pol)
cannam@160:       {
cannam@160:         if(check_dist(function, p, result, pol) == false)
cannam@160:         {
cannam@160:           return false;
cannam@160:         }
cannam@160:         if( !(boost::math::isfinite)(k) || (k < 0) )
cannam@160:         { // Check k failures.
cannam@160:           *result = policies::raise_domain_error<RealType>(
cannam@160:             function,
cannam@160:             "Number of failures argument is %1%, but must be >= 0 !", k, pol);
cannam@160:           return false;
cannam@160:         }
cannam@160:         return true;
cannam@160:       } // Check_dist_and_k
cannam@160: 
cannam@160:       template <class RealType, class Policy>
cannam@160:       inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& pol)
cannam@160:       {
cannam@160:         if((check_dist(function, p, result, pol) && detail::check_probability(function, prob, result, pol)) == false)
cannam@160:         {
cannam@160:           return false;
cannam@160:         }
cannam@160:         return true;
cannam@160:       } // check_dist_and_prob
cannam@160:     } //  namespace geometric_detail
cannam@160: 
cannam@160:     template <class RealType = double, class Policy = policies::policy<> >
cannam@160:     class geometric_distribution
cannam@160:     {
cannam@160:     public:
cannam@160:       typedef RealType value_type;
cannam@160:       typedef Policy policy_type;
cannam@160: 
cannam@160:       geometric_distribution(RealType p) : m_p(p)
cannam@160:       { // Constructor stores success_fraction p.
cannam@160:         RealType result;
cannam@160:         geometric_detail::check_dist(
cannam@160:           "geometric_distribution<%1%>::geometric_distribution",
cannam@160:           m_p, // Check success_fraction 0 <= p <= 1.
cannam@160:           &result, Policy());
cannam@160:       } // geometric_distribution constructor.
cannam@160: 
cannam@160:       // Private data getter class member functions.
cannam@160:       RealType success_fraction() const
cannam@160:       { // Probability of success as fraction in range 0 to 1.
cannam@160:         return m_p;
cannam@160:       }
cannam@160:       RealType successes() const
cannam@160:       { // Total number of successes r = 1 (for compatibility with negative binomial?).
cannam@160:         return 1;
cannam@160:       }
cannam@160: 
cannam@160:       // Parameter estimation.
cannam@160:       // (These are copies of negative_binomial distribution with successes = 1).
cannam@160:       static RealType find_lower_bound_on_p(
cannam@160:         RealType trials,
cannam@160:         RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
cannam@160:       {
cannam@160:         static const char* function = "boost::math::geometric<%1%>::find_lower_bound_on_p";
cannam@160:         RealType result = 0;  // of error checks.
cannam@160:         RealType successes = 1;
cannam@160:         RealType failures = trials - successes;
cannam@160:         if(false == detail::check_probability(function, alpha, &result, Policy())
cannam@160:           && geometric_detail::check_dist_and_k(
cannam@160:           function, RealType(0), failures, &result, Policy()))
cannam@160:         {
cannam@160:           return result;
cannam@160:         }
cannam@160:         // Use complement ibeta_inv function for lower bound.
cannam@160:         // This is adapted from the corresponding binomial formula
cannam@160:         // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
cannam@160:         // This is a Clopper-Pearson interval, and may be overly conservative,
cannam@160:         // see also "A Simple Improved Inferential Method for Some
cannam@160:         // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY
cannam@160:         // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
cannam@160:         //
cannam@160:         return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy());
cannam@160:       } // find_lower_bound_on_p
cannam@160: 
cannam@160:       static RealType find_upper_bound_on_p(
cannam@160:         RealType trials,
cannam@160:         RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
cannam@160:       {
cannam@160:         static const char* function = "boost::math::geometric<%1%>::find_upper_bound_on_p";
cannam@160:         RealType result = 0;  // of error checks.
cannam@160:         RealType successes = 1;
cannam@160:         RealType failures = trials - successes;
cannam@160:         if(false == geometric_detail::check_dist_and_k(
cannam@160:           function, RealType(0), failures, &result, Policy())
cannam@160:           && detail::check_probability(function, alpha, &result, Policy()))
cannam@160:         {
cannam@160:           return result;
cannam@160:         }
cannam@160:         if(failures == 0)
cannam@160:         {
cannam@160:            return 1;
cannam@160:         }// Use complement ibetac_inv function for upper bound.
cannam@160:         // Note adjusted failures value: *not* failures+1 as usual.
cannam@160:         // This is adapted from the corresponding binomial formula
cannam@160:         // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
cannam@160:         // This is a Clopper-Pearson interval, and may be overly conservative,
cannam@160:         // see also "A Simple Improved Inferential Method for Some
cannam@160:         // Discrete Distributions" Yong CAI and K. Krishnamoorthy
cannam@160:         // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
cannam@160:         //
cannam@160:         return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy());
cannam@160:       } // find_upper_bound_on_p
cannam@160: 
cannam@160:       // Estimate number of trials :
cannam@160:       // "How many trials do I need to be P% sure of seeing k or fewer failures?"
cannam@160: 
cannam@160:       static RealType find_minimum_number_of_trials(
cannam@160:         RealType k,     // number of failures (k >= 0).
cannam@160:         RealType p,     // success fraction 0 <= p <= 1.
cannam@160:         RealType alpha) // risk level threshold 0 <= alpha <= 1.
cannam@160:       {
cannam@160:         static const char* function = "boost::math::geometric<%1%>::find_minimum_number_of_trials";
cannam@160:         // Error checks:
cannam@160:         RealType result = 0;
cannam@160:         if(false == geometric_detail::check_dist_and_k(
cannam@160:           function, p, k, &result, Policy())
cannam@160:           && detail::check_probability(function, alpha, &result, Policy()))
cannam@160:         {
cannam@160:           return result;
cannam@160:         }
cannam@160:         result = ibeta_inva(k + 1, p, alpha, Policy());  // returns n - k
cannam@160:         return result + k;
cannam@160:       } // RealType find_number_of_failures
cannam@160: 
cannam@160:       static RealType find_maximum_number_of_trials(
cannam@160:         RealType k,     // number of failures (k >= 0).
cannam@160:         RealType p,     // success fraction 0 <= p <= 1.
cannam@160:         RealType alpha) // risk level threshold 0 <= alpha <= 1.
cannam@160:       {
cannam@160:         static const char* function = "boost::math::geometric<%1%>::find_maximum_number_of_trials";
cannam@160:         // Error checks:
cannam@160:         RealType result = 0;
cannam@160:         if(false == geometric_detail::check_dist_and_k(
cannam@160:           function, p, k, &result, Policy())
cannam@160:           &&  detail::check_probability(function, alpha, &result, Policy()))
cannam@160:         { 
cannam@160:           return result;
cannam@160:         }
cannam@160:         result = ibetac_inva(k + 1, p, alpha, Policy());  // returns n - k
cannam@160:         return result + k;
cannam@160:       } // RealType find_number_of_trials complemented
cannam@160: 
cannam@160:     private:
cannam@160:       //RealType m_r; // successes fixed at unity.
cannam@160:       RealType m_p; // success_fraction
cannam@160:     }; // template <class RealType, class Policy> class geometric_distribution
cannam@160: 
cannam@160:     typedef geometric_distribution<double> geometric; // Reserved name of type double.
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline const std::pair<RealType, RealType> range(const geometric_distribution<RealType, Policy>& /* dist */)
cannam@160:     { // Range of permissible values for random variable k.
cannam@160:        using boost::math::tools::max_value;
cannam@160:        return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer?
cannam@160:     }
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline const std::pair<RealType, RealType> support(const geometric_distribution<RealType, Policy>& /* dist */)
cannam@160:     { // Range of supported values for random variable k.
cannam@160:        // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
cannam@160:        using boost::math::tools::max_value;
cannam@160:        return std::pair<RealType, RealType>(static_cast<RealType>(0),  max_value<RealType>()); // max_integer?
cannam@160:     }
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType mean(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     { // Mean of geometric distribution = (1-p)/p.
cannam@160:       return (1 - dist.success_fraction() ) / dist.success_fraction();
cannam@160:     } // mean
cannam@160: 
cannam@160:     // median implemented via quantile(half) in derived accessors.
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType mode(const geometric_distribution<RealType, Policy>&)
cannam@160:     { // Mode of geometric distribution = zero.
cannam@160:       BOOST_MATH_STD_USING // ADL of std functions.
cannam@160:       return 0;
cannam@160:     } // mode
cannam@160:     
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType variance(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     { // Variance of Binomial distribution = (1-p) / p^2.
cannam@160:       return  (1 - dist.success_fraction())
cannam@160:         / (dist.success_fraction() * dist.success_fraction());
cannam@160:     } // variance
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType skewness(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     { // skewness of geometric distribution = 2-p / (sqrt(r(1-p))
cannam@160:       BOOST_MATH_STD_USING // ADL of std functions.
cannam@160:       RealType p = dist.success_fraction();
cannam@160:       return (2 - p) / sqrt(1 - p);
cannam@160:     } // skewness
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType kurtosis(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     { // kurtosis of geometric distribution
cannam@160:       // http://en.wikipedia.org/wiki/geometric is kurtosis_excess so add 3
cannam@160:       RealType p = dist.success_fraction();
cannam@160:       return 3 + (p*p - 6*p + 6) / (1 - p);
cannam@160:     } // kurtosis
cannam@160: 
cannam@160:      template <class RealType, class Policy>
cannam@160:     inline RealType kurtosis_excess(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     { // kurtosis excess of geometric distribution
cannam@160:       // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess
cannam@160:       RealType p = dist.success_fraction();
cannam@160:       return (p*p - 6*p + 6) / (1 - p);
cannam@160:     } // kurtosis_excess
cannam@160: 
cannam@160:     // RealType standard_deviation(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     // standard_deviation provided by derived accessors.
cannam@160:     // RealType hazard(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     // hazard of geometric distribution provided by derived accessors.
cannam@160:     // RealType chf(const geometric_distribution<RealType, Policy>& dist)
cannam@160:     // chf of geometric distribution provided by derived accessors.
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType pdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
cannam@160:     { // Probability Density/Mass Function.
cannam@160:       BOOST_FPU_EXCEPTION_GUARD
cannam@160:       BOOST_MATH_STD_USING  // For ADL of math functions.
cannam@160:       static const char* function = "boost::math::pdf(const geometric_distribution<%1%>&, %1%)";
cannam@160: 
cannam@160:       RealType p = dist.success_fraction();
cannam@160:       RealType result = 0;
cannam@160:       if(false == geometric_detail::check_dist_and_k(
cannam@160:         function,
cannam@160:         p,
cannam@160:         k,
cannam@160:         &result, Policy()))
cannam@160:       {
cannam@160:         return result;
cannam@160:       }
cannam@160:       if (k == 0)
cannam@160:       {
cannam@160:         return p; // success_fraction
cannam@160:       }
cannam@160:       RealType q = 1 - p;  // Inaccurate for small p?
cannam@160:       // So try to avoid inaccuracy for large or small p.
cannam@160:       // but has little effect > last significant bit.
cannam@160:       //cout << "p *  pow(q, k) " << result << endl; // seems best whatever p
cannam@160:       //cout << "exp(p * k * log1p(-p)) " << p * exp(k * log1p(-p)) << endl;
cannam@160:       //if (p < 0.5)
cannam@160:       //{
cannam@160:       //  result = p *  pow(q, k);
cannam@160:       //}
cannam@160:       //else
cannam@160:       //{
cannam@160:       //  result = p * exp(k * log1p(-p));
cannam@160:       //}
cannam@160:       result = p * pow(q, k);
cannam@160:       return result;
cannam@160:     } // geometric_pdf
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType cdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
cannam@160:     { // Cumulative Distribution Function of geometric.
cannam@160:       static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
cannam@160: 
cannam@160:       // k argument may be integral, signed, or unsigned, or floating point.
cannam@160:       // If necessary, it has already been promoted from an integral type.
cannam@160:       RealType p = dist.success_fraction();
cannam@160:       // Error check:
cannam@160:       RealType result = 0;
cannam@160:       if(false == geometric_detail::check_dist_and_k(
cannam@160:         function,
cannam@160:         p,
cannam@160:         k,
cannam@160:         &result, Policy()))
cannam@160:       {
cannam@160:         return result;
cannam@160:       }
cannam@160:       if(k == 0)
cannam@160:       {
cannam@160:         return p; // success_fraction
cannam@160:       }
cannam@160:       //RealType q = 1 - p;  // Bad for small p
cannam@160:       //RealType probability = 1 - std::pow(q, k+1);
cannam@160: 
cannam@160:       RealType z = boost::math::log1p(-p, Policy()) * (k + 1);
cannam@160:       RealType probability = -boost::math::expm1(z, Policy());
cannam@160: 
cannam@160:       return probability;
cannam@160:     } // cdf Cumulative Distribution Function geometric.
cannam@160: 
cannam@160:       template <class RealType, class Policy>
cannam@160:       inline RealType cdf(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c)
cannam@160:       { // Complemented Cumulative Distribution Function geometric.
cannam@160:       BOOST_MATH_STD_USING
cannam@160:       static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
cannam@160:       // k argument may be integral, signed, or unsigned, or floating point.
cannam@160:       // If necessary, it has already been promoted from an integral type.
cannam@160:       RealType const& k = c.param;
cannam@160:       geometric_distribution<RealType, Policy> const& dist = c.dist;
cannam@160:       RealType p = dist.success_fraction();
cannam@160:       // Error check:
cannam@160:       RealType result = 0;
cannam@160:       if(false == geometric_detail::check_dist_and_k(
cannam@160:         function,
cannam@160:         p,
cannam@160:         k,
cannam@160:         &result, Policy()))
cannam@160:       {
cannam@160:         return result;
cannam@160:       }
cannam@160:       RealType z = boost::math::log1p(-p, Policy()) * (k+1);
cannam@160:       RealType probability = exp(z);
cannam@160:       return probability;
cannam@160:     } // cdf Complemented Cumulative Distribution Function geometric.
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType quantile(const geometric_distribution<RealType, Policy>& dist, const RealType& x)
cannam@160:     { // Quantile, percentile/100 or Percent Point geometric function.
cannam@160:       // Return the number of expected failures k for a given probability p.
cannam@160: 
cannam@160:       // Inverse cumulative Distribution Function or Quantile (percentile / 100) of geometric Probability.
cannam@160:       // k argument may be integral, signed, or unsigned, or floating point.
cannam@160: 
cannam@160:       static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)";
cannam@160:       BOOST_MATH_STD_USING // ADL of std functions.
cannam@160: 
cannam@160:       RealType success_fraction = dist.success_fraction();
cannam@160:       // Check dist and x.
cannam@160:       RealType result = 0;
cannam@160:       if(false == geometric_detail::check_dist_and_prob
cannam@160:         (function, success_fraction, x, &result, Policy()))
cannam@160:       {
cannam@160:         return result;
cannam@160:       }
cannam@160: 
cannam@160:       // Special cases.
cannam@160:       if (x == 1)
cannam@160:       {  // Would need +infinity failures for total confidence.
cannam@160:         result = policies::raise_overflow_error<RealType>(
cannam@160:             function,
cannam@160:             "Probability argument is 1, which implies infinite failures !", Policy());
cannam@160:         return result;
cannam@160:        // usually means return +std::numeric_limits<RealType>::infinity();
cannam@160:        // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
cannam@160:       }
cannam@160:       if (x == 0)
cannam@160:       { // No failures are expected if P = 0.
cannam@160:         return 0; // Total trials will be just dist.successes.
cannam@160:       }
cannam@160:       // if (P <= pow(dist.success_fraction(), 1))
cannam@160:       if (x <= success_fraction)
cannam@160:       { // p <= pdf(dist, 0) == cdf(dist, 0)
cannam@160:         return 0;
cannam@160:       }
cannam@160:       if (x == 1)
cannam@160:       {
cannam@160:         return 0;
cannam@160:       }
cannam@160:    
cannam@160:       // log(1-x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small
cannam@160:       result = boost::math::log1p(-x, Policy()) / boost::math::log1p(-success_fraction, Policy()) - 1;
cannam@160:       // Subtract a few epsilons here too?
cannam@160:       // to make sure it doesn't slip over, so ceil would be one too many.
cannam@160:       return result;
cannam@160:     } // RealType quantile(const geometric_distribution dist, p)
cannam@160: 
cannam@160:     template <class RealType, class Policy>
cannam@160:     inline RealType quantile(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c)
cannam@160:     {  // Quantile or Percent Point Binomial function.
cannam@160:        // Return the number of expected failures k for a given
cannam@160:        // complement of the probability Q = 1 - P.
cannam@160:        static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)";
cannam@160:        BOOST_MATH_STD_USING
cannam@160:        // Error checks:
cannam@160:        RealType x = c.param;
cannam@160:        const geometric_distribution<RealType, Policy>& dist = c.dist;
cannam@160:        RealType success_fraction = dist.success_fraction();
cannam@160:        RealType result = 0;
cannam@160:        if(false == geometric_detail::check_dist_and_prob(
cannam@160:           function,
cannam@160:           success_fraction,
cannam@160:           x,
cannam@160:           &result, Policy()))
cannam@160:        {
cannam@160:           return result;
cannam@160:        }
cannam@160: 
cannam@160:        // Special cases:
cannam@160:        if(x == 1)
cannam@160:        {  // There may actually be no answer to this question,
cannam@160:           // since the probability of zero failures may be non-zero,
cannam@160:           return 0; // but zero is the best we can do:
cannam@160:        }
cannam@160:        if (-x <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy()))
cannam@160:        {  // q <= cdf(complement(dist, 0)) == pdf(dist, 0)
cannam@160:           return 0; //
cannam@160:        }
cannam@160:        if(x == 0)
cannam@160:        {  // Probability 1 - Q  == 1 so infinite failures to achieve certainty.
cannam@160:           // Would need +infinity failures for total confidence.
cannam@160:           result = policies::raise_overflow_error<RealType>(
cannam@160:              function,
cannam@160:              "Probability argument complement is 0, which implies infinite failures !", Policy());
cannam@160:           return result;
cannam@160:           // usually means return +std::numeric_limits<RealType>::infinity();
cannam@160:           // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
cannam@160:        }
cannam@160:        // log(x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small
cannam@160:        result = log(x) / boost::math::log1p(-success_fraction, Policy()) - 1;
cannam@160:       return result;
cannam@160: 
cannam@160:     } // quantile complement
cannam@160: 
cannam@160:  } // namespace math
cannam@160: } // namespace boost
cannam@160: 
cannam@160: // This include must be at the end, *after* the accessors
cannam@160: // for this distribution have been defined, in order to
cannam@160: // keep compilers that support two-phase lookup happy.
cannam@160: #include <boost/math/distributions/detail/derived_accessors.hpp>
cannam@160: 
cannam@160: #if defined (BOOST_MSVC)
cannam@160: # pragma warning(pop)
cannam@160: #endif
cannam@160: 
cannam@160: #endif // BOOST_MATH_SPECIAL_GEOMETRIC_HPP