// 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;
|
|
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
|
