boost/math/distributions/uniform.hpp
// 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 l_lower = 0, RealType l_upper = 1) // Constructor.
: m_lower(l_lower), m_upper(l_upper) // Default is standard uniform distribution.
{
RealType result;
detail::check_uniform("boost::math::uniform_distribution<%1%>::uniform_distribution", l_lower, l_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;
#ifdef __cpp_deduction_guides
template <class RealType>
uniform_distribution(RealType)->uniform_distribution<typename boost::math::tools::promote_args<RealType>::type>;
template <class RealType>
uniform_distribution(RealType,RealType)->uniform_distribution<typename boost::math::tools::promote_args<RealType>::type>;
#endif
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 = 0; // 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 = 0; // 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 = 0; // 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 = 0; // 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 1;
}
if (x > upper)
{
return 0;
}
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 = 0; // 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()))
{
return result;
}
if(q == 0)
{
return upper;
}
if(q == 1)
{
return lower;
}
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 = 0; // 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 = 0; // 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 = 0; // 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 = 0; // 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 = 0; // 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 = 0; // 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;
}
template <class RealType, class Policy>
inline RealType entropy(const uniform_distribution<RealType, Policy>& dist)
{
using std::log;
return log(dist.upper() - dist.lower());
}
} // 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