// Copyright John Maddock 2006. | |
// Copyright Paul A. Bristow 2006. | |
// 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) | |
// TODO deal with infinity as special better - or remove. | |
// | |
#ifndef BOOST_STATS_UNIFORM_HPP | |
#define BOOST_STATS_UNIFORM_HPP | |
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm | |
// http://mathworld.wolfram.com/UniformDistribution.html | |
// http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/UniformDistribution.html | |
// http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 | |
#include <boost/math/distributions/fwd.hpp> | |
#include <boost/math/distributions/detail/common_error_handling.hpp> | |
#include <boost/math/distributions/complement.hpp> | |
#include <utility> | |
namespace boost{ namespace math | |
{ | |
namespace detail | |
{ | |
template <class RealType, class Policy> | |
inline bool check_uniform_lower( | |
const char* function, | |
RealType lower, | |
RealType* result, const Policy& pol) | |
{ | |
if((boost::math::isfinite)(lower)) | |
{ // any finite value is OK. | |
return true; | |
} | |
else | |
{ // Not finite. | |
*result = policies::raise_domain_error<RealType>( | |
function, | |
"Lower parameter is %1%, but must be finite!", lower, pol); | |
return false; | |
} | |
} // bool check_uniform_lower( | |
template <class RealType, class Policy> | |
inline bool check_uniform_upper( | |
const char* function, | |
RealType upper, | |
RealType* result, const Policy& pol) | |
{ | |
if((boost::math::isfinite)(upper)) | |
{ // Any finite value is OK. | |
return true; | |
} | |
else | |
{ // Not finite. | |
*result = policies::raise_domain_error<RealType>( | |
function, | |
"Upper parameter is %1%, but must be finite!", upper, pol); | |
return false; | |
} | |
} // bool check_uniform_upper( | |
template <class RealType, class Policy> | |
inline bool check_uniform_x( | |
const char* function, | |
RealType const& x, | |
RealType* result, const Policy& pol) | |
{ | |
if((boost::math::isfinite)(x)) | |
{ // Any finite value is OK | |
return true; | |
} | |
else | |
{ // Not finite.. | |
*result = policies::raise_domain_error<RealType>( | |
function, | |
"x parameter is %1%, but must be finite!", x, pol); | |
return false; | |
} | |
} // bool check_uniform_x | |
template <class RealType, class Policy> | |
inline bool check_uniform( | |
const char* function, | |
RealType lower, | |
RealType upper, | |
RealType* result, const Policy& pol) | |
{ | |
if((check_uniform_lower(function, lower, result, pol) == false) | |
|| (check_uniform_upper(function, upper, result, pol) == false)) | |
{ | |
return false; | |
} | |
else if (lower >= upper) // If lower == upper then 1 / (upper-lower) = 1/0 = +infinity! | |
{ // upper and lower have been checked before, so must be lower >= upper. | |
*result = policies::raise_domain_error<RealType>( | |
function, | |
"lower parameter is %1%, but must be less than upper!", lower, pol); | |
return false; | |
} | |
else | |
{ // All OK, | |
return true; | |
} | |
} // bool check_uniform( | |
} // namespace detail | |
template <class RealType = double, class Policy = policies::policy<> > | |
class uniform_distribution | |
{ | |
public: | |
typedef RealType value_type; | |
typedef Policy policy_type; | |
uniform_distribution(RealType lower = 0, RealType upper = 1) // Constructor. | |
: m_lower(lower), m_upper(upper) // Default is standard uniform distribution. | |
{ | |
RealType result; | |
detail::check_uniform("boost::math::uniform_distribution<%1%>::uniform_distribution", lower, upper, &result, Policy()); | |
} | |
// Accessor functions. | |
RealType lower()const | |
{ | |
return m_lower; | |
} | |
RealType upper()const | |
{ | |
return m_upper; | |
} | |
private: | |
// Data members: | |
RealType m_lower; // distribution lower aka a. | |
RealType m_upper; // distribution upper aka b. | |
}; // class uniform_distribution | |
typedef uniform_distribution<double> uniform; | |
template <class RealType, class Policy> | |
inline const std::pair<RealType, RealType> range(const uniform_distribution<RealType, Policy>& /* dist */) | |
{ // Range of permissible values for random variable x. | |
using boost::math::tools::max_value; | |
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + 'infinity'. | |
// Note RealType infinity is NOT permitted, only max_value. | |
} | |
template <class RealType, class Policy> | |
inline const std::pair<RealType, RealType> support(const uniform_distribution<RealType, Policy>& dist) | |
{ // Range of supported values for random variable x. | |
// 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>(dist.lower(), dist.upper()); | |
} | |
template <class RealType, class Policy> | |
inline RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_uniform_x("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy())) | |
{ | |
return result; | |
} | |
if((x < lower) || (x > upper) ) | |
{ | |
return 0; | |
} | |
else | |
{ | |
return 1 / (upper - lower); | |
} | |
} // RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) | |
template <class RealType, class Policy> | |
inline RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy())) | |
{ | |
return result; | |
} | |
if (x < lower) | |
{ | |
return 0; | |
} | |
if (x > upper) | |
{ | |
return 1; | |
} | |
return (x - lower) / (upper - lower); // lower <= x <= upper | |
} // RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) | |
template <class RealType, class Policy> | |
inline RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks | |
if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", p, &result, Policy())) | |
{ | |
return result; | |
} | |
if(p == 0) | |
{ | |
return lower; | |
} | |
if(p == 1) | |
{ | |
return upper; | |
} | |
return p * (upper - lower) + lower; | |
} // RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p) | |
template <class RealType, class Policy> | |
inline RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) | |
{ | |
RealType lower = c.dist.lower(); | |
RealType upper = c.dist.upper(); | |
RealType x = c.param; | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy())) | |
{ | |
return result; | |
} | |
if (x < lower) | |
{ | |
return 0; | |
} | |
if (x > upper) | |
{ | |
return 1; | |
} | |
return (upper - x) / (upper - lower); | |
} // RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) | |
template <class RealType, class Policy> | |
inline RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) | |
{ | |
RealType lower = c.dist.lower(); | |
RealType upper = c.dist.upper(); | |
RealType q = c.param; | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", q, &result, Policy())) | |
if(q == 0) | |
{ | |
return lower; | |
} | |
if(q == 1) | |
{ | |
return upper; | |
} | |
return -q * (upper - lower) + upper; | |
} // RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) | |
template <class RealType, class Policy> | |
inline RealType mean(const uniform_distribution<RealType, Policy>& dist) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::mean(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
return (lower + upper ) / 2; | |
} // RealType mean(const uniform_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType variance(const uniform_distribution<RealType, Policy>& dist) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::variance(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
return (upper - lower) * ( upper - lower) / 12; | |
// for standard uniform = 0.833333333333333333333333333333333333333333; | |
} // RealType variance(const uniform_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType mode(const uniform_distribution<RealType, Policy>& dist) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::mode(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
result = lower; // Any value [lower, upper] but arbitrarily choose lower. | |
return result; | |
} | |
template <class RealType, class Policy> | |
inline RealType median(const uniform_distribution<RealType, Policy>& dist) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::median(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
return (lower + upper) / 2; // | |
} | |
template <class RealType, class Policy> | |
inline RealType skewness(const uniform_distribution<RealType, Policy>& dist) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::skewness(const uniform_distribution<%1%>&)",lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
return 0; | |
} // RealType skewness(const uniform_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist) | |
{ | |
RealType lower = dist.lower(); | |
RealType upper = dist.upper(); | |
RealType result; // of checks. | |
if(false == detail::check_uniform("boost::math::kurtosis_execess(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) | |
{ | |
return result; | |
} | |
return static_cast<RealType>(-6)/5; // -6/5 = -1.2; | |
} // RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType kurtosis(const uniform_distribution<RealType, Policy>& dist) | |
{ | |
return kurtosis_excess(dist) + 3; | |
} | |
} // 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> | |
#endif // BOOST_STATS_UNIFORM_HPP | |