517 lines
21 KiB
C++
517 lines
21 KiB
C++
|
// boost\math\distributions\geometric.hpp
|
||
|
|
|
||
|
|
// Copyright John Maddock 2010.
|
||
|
|
// Copyright Paul A. Bristow 2010.
|
||
|
|
|
||
|
|
// 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)
|
||
|
|
|
||
|
|
// geometric distribution is a discrete probability distribution.
|
||
|
|
// It expresses the probability distribution of the number (k) of
|
||
|
|
// events, occurrences, failures or arrivals before the first success.
|
||
|
|
// supported on the set {0, 1, 2, 3...}
|
||
|
|
|
||
|
|
// Note that the set includes zero (unlike some definitions that start at one).
|
||
|
|
|
||
|
|
// The random variate k is the number of events, occurrences or arrivals.
|
||
|
|
// k argument may be integral, signed, or unsigned, or floating point.
|
||
|
|
// If necessary, it has already been promoted from an integral type.
|
||
|
|
|
||
|
|
// Note that the geometric distribution
|
||
|
|
// (like others including the binomial, geometric & Bernoulli)
|
||
|
|
// is strictly defined as a discrete function:
|
||
|
|
// only integral values of k are envisaged.
|
||
|
|
// However because the method of calculation uses a continuous gamma function,
|
||
|
|
// it is convenient to treat it as if a continous function,
|
||
|
|
// and permit non-integral values of k.
|
||
|
|
// To enforce the strict mathematical model, users should use floor or ceil functions
|
||
|
|
// on k outside this function to ensure that k is integral.
|
||
|
|
|
||
|
|
// See http://en.wikipedia.org/wiki/geometric_distribution
|
||
|
|
// http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html
|
||
|
|
// http://mathworld.wolfram.com/GeometricDistribution.html
|
||
|
|
|
||
|
|
#ifndef BOOST_MATH_SPECIAL_GEOMETRIC_HPP
|
||
|
|
#define BOOST_MATH_SPECIAL_GEOMETRIC_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 geometric_detail
|
||
|
|
{
|
||
|
|
// Common error checking routines for geometric distribution function:
|
||
|
|
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& p, RealType* result, const Policy& pol)
|
||
|
|
{
|
||
|
|
return check_success_fraction(function, p, result, pol);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol)
|
||
|
|
{
|
||
|
|
if(check_dist(function, 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, RealType p, RealType prob, RealType* result, const Policy& pol)
|
||
|
|
{
|
||
|
|
if((check_dist(function, p, result, pol) && detail::check_probability(function, prob, result, pol)) == false)
|
||
|
|
{
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
} // check_dist_and_prob
|
||
|
|
} // namespace geometric_detail
|
||
|
|
|
||
|
|
template <class RealType = double, class Policy = policies::policy<> >
|
||
|
|
class geometric_distribution
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef RealType value_type;
|
||
|
|
typedef Policy policy_type;
|
||
|
|
|
||
|
|
geometric_distribution(RealType p) : m_p(p)
|
||
|
|
{ // Constructor stores success_fraction p.
|
||
|
|
RealType result;
|
||
|
|
geometric_detail::check_dist(
|
||
|
|
"geometric_distribution<%1%>::geometric_distribution",
|
||
|
|
m_p, // Check success_fraction 0 <= p <= 1.
|
||
|
|
&result, Policy());
|
||
|
|
} // geometric_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 = 1 (for compatibility with negative binomial?).
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Parameter estimation.
|
||
|
|
// (These are copies of negative_binomial distribution with successes = 1).
|
||
|
|
static RealType find_lower_bound_on_p(
|
||
|
|
RealType trials,
|
||
|
|
RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
|
||
|
|
{
|
||
|
|
static const char* function = "boost::math::geometric<%1%>::find_lower_bound_on_p";
|
||
|
|
RealType result = 0; // of error checks.
|
||
|
|
RealType successes = 1;
|
||
|
|
RealType failures = trials - successes;
|
||
|
|
if(false == detail::check_probability(function, alpha, &result, Policy())
|
||
|
|
&& geometric_detail::check_dist_and_k(
|
||
|
|
function, 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 alpha) // alpha 0.05 equivalent to 95% for one-sided test.
|
||
|
|
{
|
||
|
|
static const char* function = "boost::math::geometric<%1%>::find_upper_bound_on_p";
|
||
|
|
RealType result = 0; // of error checks.
|
||
|
|
RealType successes = 1;
|
||
|
|
RealType failures = trials - successes;
|
||
|
|
if(false == geometric_detail::check_dist_and_k(
|
||
|
|
function, 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::geometric<%1%>::find_minimum_number_of_trials";
|
||
|
|
// Error checks:
|
||
|
|
RealType result = 0;
|
||
|
|
if(false == geometric_detail::check_dist_and_k(
|
||
|
|
function, 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::geometric<%1%>::find_maximum_number_of_trials";
|
||
|
|
// Error checks:
|
||
|
|
RealType result = 0;
|
||
|
|
if(false == geometric_detail::check_dist_and_k(
|
||
|
|
function, 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 fixed at unity.
|
||
|
|
RealType m_p; // success_fraction
|
||
|
|
}; // template <class RealType, class Policy> class geometric_distribution
|
||
|
|
|
||
|
|
typedef geometric_distribution<double> geometric; // Reserved name of type double.
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline const std::pair<RealType, RealType> range(const geometric_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 geometric_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 geometric_distribution<RealType, Policy>& dist)
|
||
|
|
{ // Mean of geometric distribution = (1-p)/p.
|
||
|
|
return (1 - dist.success_fraction() ) / dist.success_fraction();
|
||
|
|
} // mean
|
||
|
|
|
||
|
|
// median implemented via quantile(half) in derived accessors.
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType mode(const geometric_distribution<RealType, Policy>&)
|
||
|
|
{ // Mode of geometric distribution = zero.
|
||
|
|
BOOST_MATH_STD_USING // ADL of std functions.
|
||
|
|
return 0;
|
||
|
|
} // mode
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType variance(const geometric_distribution<RealType, Policy>& dist)
|
||
|
|
{ // Variance of Binomial distribution = (1-p) / p^2.
|
||
|
|
return (1 - dist.success_fraction())
|
||
|
|
/ (dist.success_fraction() * dist.success_fraction());
|
||
|
|
} // variance
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType skewness(const geometric_distribution<RealType, Policy>& dist)
|
||
|
|
{ // skewness of geometric distribution = 2-p / (sqrt(r(1-p))
|
||
|
|
BOOST_MATH_STD_USING // ADL of std functions.
|
||
|
|
RealType p = dist.success_fraction();
|
||
|
|
return (2 - p) / sqrt(1 - p);
|
||
|
|
} // skewness
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis(const geometric_distribution<RealType, Policy>& dist)
|
||
|
|
{ // kurtosis of geometric distribution
|
||
|
|
// http://en.wikipedia.org/wiki/geometric is kurtosis_excess so add 3
|
||
|
|
RealType p = dist.success_fraction();
|
||
|
|
return 3 + (p*p - 6*p + 6) / (1 - p);
|
||
|
|
} // kurtosis
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis_excess(const geometric_distribution<RealType, Policy>& dist)
|
||
|
|
{ // kurtosis excess of geometric distribution
|
||
|
|
// http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess
|
||
|
|
RealType p = dist.success_fraction();
|
||
|
|
return (p*p - 6*p + 6) / (1 - p);
|
||
|
|
} // kurtosis_excess
|
||
|
|
|
||
|
|
// RealType standard_deviation(const geometric_distribution<RealType, Policy>& dist)
|
||
|
|
// standard_deviation provided by derived accessors.
|
||
|
|
// RealType hazard(const geometric_distribution<RealType, Policy>& dist)
|
||
|
|
// hazard of geometric distribution provided by derived accessors.
|
||
|
|
// RealType chf(const geometric_distribution<RealType, Policy>& dist)
|
||
|
|
// chf of geometric distribution provided by derived accessors.
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType pdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
|
||
|
|
{ // Probability Density/Mass Function.
|
||
|
|
BOOST_FPU_EXCEPTION_GUARD
|
||
|
|
BOOST_MATH_STD_USING // For ADL of math functions.
|
||
|
|
static const char* function = "boost::math::pdf(const geometric_distribution<%1%>&, %1%)";
|
||
|
|
|
||
|
|
RealType p = dist.success_fraction();
|
||
|
|
RealType result = 0;
|
||
|
|
if(false == geometric_detail::check_dist_and_k(
|
||
|
|
function,
|
||
|
|
p,
|
||
|
|
k,
|
||
|
|
&result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
if (k == 0)
|
||
|
|
{
|
||
|
|
return p; // success_fraction
|
||
|
|
}
|
||
|
|
RealType q = 1 - p; // Inaccurate for small p?
|
||
|
|
// So try to avoid inaccuracy for large or small p.
|
||
|
|
// but has little effect > last significant bit.
|
||
|
|
//cout << "p * pow(q, k) " << result << endl; // seems best whatever p
|
||
|
|
//cout << "exp(p * k * log1p(-p)) " << p * exp(k * log1p(-p)) << endl;
|
||
|
|
//if (p < 0.5)
|
||
|
|
//{
|
||
|
|
// result = p * pow(q, k);
|
||
|
|
//}
|
||
|
|
//else
|
||
|
|
//{
|
||
|
|
// result = p * exp(k * log1p(-p));
|
||
|
|
//}
|
||
|
|
result = p * pow(q, k);
|
||
|
|
return result;
|
||
|
|
} // geometric_pdf
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType cdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
|
||
|
|
{ // Cumulative Distribution Function of geometric.
|
||
|
|
static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
|
||
|
|
|
||
|
|
// 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();
|
||
|
|
// Error check:
|
||
|
|
RealType result = 0;
|
||
|
|
if(false == geometric_detail::check_dist_and_k(
|
||
|
|
function,
|
||
|
|
p,
|
||
|
|
k,
|
||
|
|
&result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
if(k == 0)
|
||
|
|
{
|
||
|
|
return p; // success_fraction
|
||
|
|
}
|
||
|
|
//RealType q = 1 - p; // Bad for small p
|
||
|
|
//RealType probability = 1 - std::pow(q, k+1);
|
||
|
|
|
||
|
|
RealType z = boost::math::log1p(-p, Policy()) * (k + 1);
|
||
|
|
RealType probability = -boost::math::expm1(z, Policy());
|
||
|
|
|
||
|
|
return probability;
|
||
|
|
} // cdf Cumulative Distribution Function geometric.
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType cdf(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c)
|
||
|
|
{ // Complemented Cumulative Distribution Function geometric.
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
|
||
|
|
// 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;
|
||
|
|
geometric_distribution<RealType, Policy> const& dist = c.dist;
|
||
|
|
RealType p = dist.success_fraction();
|
||
|
|
// Error check:
|
||
|
|
RealType result = 0;
|
||
|
|
if(false == geometric_detail::check_dist_and_k(
|
||
|
|
function,
|
||
|
|
p,
|
||
|
|
k,
|
||
|
|
&result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
RealType z = boost::math::log1p(-p, Policy()) * (k+1);
|
||
|
|
RealType probability = exp(z);
|
||
|
|
return probability;
|
||
|
|
} // cdf Complemented Cumulative Distribution Function geometric.
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType quantile(const geometric_distribution<RealType, Policy>& dist, const RealType& x)
|
||
|
|
{ // Quantile, percentile/100 or Percent Point geometric function.
|
||
|
|
// Return the number of expected failures k for a given probability p.
|
||
|
|
|
||
|
|
// Inverse cumulative Distribution Function or Quantile (percentile / 100) of geometric Probability.
|
||
|
|
// k argument may be integral, signed, or unsigned, or floating point.
|
||
|
|
|
||
|
|
static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)";
|
||
|
|
BOOST_MATH_STD_USING // ADL of std functions.
|
||
|
|
|
||
|
|
RealType success_fraction = dist.success_fraction();
|
||
|
|
// Check dist and x.
|
||
|
|
RealType result = 0;
|
||
|
|
if(false == geometric_detail::check_dist_and_prob
|
||
|
|
(function, success_fraction, x, &result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Special cases.
|
||
|
|
if (x == 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 (x == 0)
|
||
|
|
{ // No failures are expected if P = 0.
|
||
|
|
return 0; // Total trials will be just dist.successes.
|
||
|
|
}
|
||
|
|
// if (P <= pow(dist.success_fraction(), 1))
|
||
|
|
if (x <= success_fraction)
|
||
|
|
{ // p <= pdf(dist, 0) == cdf(dist, 0)
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
if (x == 1)
|
||
|
|
{
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// log(1-x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small
|
||
|
|
result = boost::math::log1p(-x, Policy()) / boost::math::log1p(-success_fraction, Policy()) - 1;
|
||
|
|
// Subtract a few epsilons here too?
|
||
|
|
// to make sure it doesn't slip over, so ceil would be one too many.
|
||
|
|
return result;
|
||
|
|
} // RealType quantile(const geometric_distribution dist, p)
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType quantile(const complemented2_type<geometric_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 geometric_distribution<%1%>&, %1%)";
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
// Error checks:
|
||
|
|
RealType x = c.param;
|
||
|
|
const geometric_distribution<RealType, Policy>& dist = c.dist;
|
||
|
|
RealType success_fraction = dist.success_fraction();
|
||
|
|
RealType result = 0;
|
||
|
|
if(false == geometric_detail::check_dist_and_prob(
|
||
|
|
function,
|
||
|
|
success_fraction,
|
||
|
|
x,
|
||
|
|
&result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Special cases:
|
||
|
|
if(x == 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 (-x <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy()))
|
||
|
|
{ // q <= cdf(complement(dist, 0)) == pdf(dist, 0)
|
||
|
|
return 0; //
|
||
|
|
}
|
||
|
|
if(x == 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
|
||
|
|
}
|
||
|
|
// log(x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small
|
||
|
|
result = log(x) / boost::math::log1p(-success_fraction, Policy()) - 1;
|
||
|
|
return result;
|
||
|
|
|
||
|
|
} // 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_GEOMETRIC_HPP
|