383 lines
13 KiB
Plaintext
383 lines
13 KiB
Plaintext
// Copyright John Maddock 2006.
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// Copyright Paul A. Bristow 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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// TODO deal with infinity as special better - or remove.
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//
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#ifndef BOOST_STATS_UNIFORM_HPP
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#define BOOST_STATS_UNIFORM_HPP
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
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// http://mathworld.wolfram.com/UniformDistribution.html
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// http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/UniformDistribution.html
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// http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/distributions/detail/common_error_handling.hpp>
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#include <boost/math/distributions/complement.hpp>
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#include <utility>
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namespace boost{ namespace math
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{
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namespace detail
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{
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template <class RealType, class Policy>
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inline bool check_uniform_lower(
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const char* function,
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RealType lower,
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RealType* result, const Policy& pol)
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{
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if((boost::math::isfinite)(lower))
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{ // any finite value is OK.
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return true;
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}
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else
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{ // Not finite.
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*result = policies::raise_domain_error<RealType>(
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function,
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"Lower parameter is %1%, but must be finite!", lower, pol);
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return false;
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}
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} // bool check_uniform_lower(
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template <class RealType, class Policy>
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inline bool check_uniform_upper(
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const char* function,
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RealType upper,
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RealType* result, const Policy& pol)
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{
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if((boost::math::isfinite)(upper))
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{ // Any finite value is OK.
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return true;
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}
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else
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{ // Not finite.
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*result = policies::raise_domain_error<RealType>(
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function,
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"Upper parameter is %1%, but must be finite!", upper, pol);
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return false;
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}
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} // bool check_uniform_upper(
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template <class RealType, class Policy>
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inline bool check_uniform_x(
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const char* function,
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RealType const& x,
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RealType* result, const Policy& pol)
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{
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if((boost::math::isfinite)(x))
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{ // Any finite value is OK
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return true;
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}
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else
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{ // Not finite..
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*result = policies::raise_domain_error<RealType>(
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function,
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"x parameter is %1%, but must be finite!", x, pol);
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return false;
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}
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} // bool check_uniform_x
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template <class RealType, class Policy>
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inline bool check_uniform(
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const char* function,
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RealType lower,
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RealType upper,
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RealType* result, const Policy& pol)
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{
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if((check_uniform_lower(function, lower, result, pol) == false)
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|| (check_uniform_upper(function, upper, result, pol) == false))
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{
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return false;
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}
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else if (lower >= upper) // If lower == upper then 1 / (upper-lower) = 1/0 = +infinity!
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{ // upper and lower have been checked before, so must be lower >= upper.
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*result = policies::raise_domain_error<RealType>(
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function,
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"lower parameter is %1%, but must be less than upper!", lower, pol);
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return false;
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}
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else
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{ // All OK,
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return true;
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}
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} // bool check_uniform(
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} // namespace detail
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template <class RealType = double, class Policy = policies::policy<> >
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class uniform_distribution
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{
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public:
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typedef RealType value_type;
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typedef Policy policy_type;
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uniform_distribution(RealType l_lower = 0, RealType l_upper = 1) // Constructor.
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: m_lower(l_lower), m_upper(l_upper) // Default is standard uniform distribution.
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{
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RealType result;
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detail::check_uniform("boost::math::uniform_distribution<%1%>::uniform_distribution", l_lower, l_upper, &result, Policy());
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}
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// Accessor functions.
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RealType lower()const
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{
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return m_lower;
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}
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RealType upper()const
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{
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return m_upper;
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}
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private:
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// Data members:
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RealType m_lower; // distribution lower aka a.
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RealType m_upper; // distribution upper aka b.
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}; // class uniform_distribution
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typedef uniform_distribution<double> uniform;
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const uniform_distribution<RealType, Policy>& /* dist */)
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{ // Range of permissible values for random variable x.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + 'infinity'.
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// Note RealType infinity is NOT permitted, only max_value.
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}
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> support(const uniform_distribution<RealType, Policy>& dist)
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{ // Range of supported values for random variable x.
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// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(dist.lower(), dist.upper());
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}
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template <class RealType, class Policy>
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inline RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_uniform_x("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy()))
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{
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return result;
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}
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if((x < lower) || (x > upper) )
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{
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return 0;
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}
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else
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{
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return 1 / (upper - lower);
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}
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} // RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
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template <class RealType, class Policy>
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inline RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy()))
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{
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return result;
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}
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if (x < lower)
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{
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return 0;
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}
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if (x > upper)
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{
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return 1;
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}
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return (x - lower) / (upper - lower); // lower <= x <= upper
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} // RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x)
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template <class RealType, class Policy>
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inline RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks
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if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", p, &result, Policy()))
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{
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return result;
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}
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if(p == 0)
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{
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return lower;
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}
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if(p == 1)
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{
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return upper;
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}
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return p * (upper - lower) + lower;
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} // RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p)
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
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{
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RealType lower = c.dist.lower();
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RealType upper = c.dist.upper();
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RealType x = c.param;
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy()))
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{
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return result;
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}
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if (x < lower)
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{
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return 1;
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}
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if (x > upper)
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{
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return 0;
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}
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return (upper - x) / (upper - lower);
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} // RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
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template <class RealType, class Policy>
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inline RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
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{
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RealType lower = c.dist.lower();
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RealType upper = c.dist.upper();
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RealType q = c.param;
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", q, &result, Policy()))
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{
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return result;
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}
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if(q == 0)
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{
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return upper;
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}
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if(q == 1)
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{
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return lower;
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}
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return -q * (upper - lower) + upper;
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} // RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c)
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template <class RealType, class Policy>
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inline RealType mean(const uniform_distribution<RealType, Policy>& dist)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::mean(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
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{
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return result;
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}
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return (lower + upper ) / 2;
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} // RealType mean(const uniform_distribution<RealType, Policy>& dist)
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template <class RealType, class Policy>
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inline RealType variance(const uniform_distribution<RealType, Policy>& dist)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::variance(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
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{
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return result;
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}
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return (upper - lower) * ( upper - lower) / 12;
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// for standard uniform = 0.833333333333333333333333333333333333333333;
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} // RealType variance(const uniform_distribution<RealType, Policy>& dist)
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template <class RealType, class Policy>
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inline RealType mode(const uniform_distribution<RealType, Policy>& dist)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::mode(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
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{
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return result;
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}
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result = lower; // Any value [lower, upper] but arbitrarily choose lower.
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return result;
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}
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template <class RealType, class Policy>
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inline RealType median(const uniform_distribution<RealType, Policy>& dist)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::median(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
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{
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return result;
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}
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return (lower + upper) / 2; //
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}
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template <class RealType, class Policy>
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inline RealType skewness(const uniform_distribution<RealType, Policy>& dist)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::skewness(const uniform_distribution<%1%>&)",lower, upper, &result, Policy()))
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{
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return result;
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}
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return 0;
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} // RealType skewness(const uniform_distribution<RealType, Policy>& dist)
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist)
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{
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RealType lower = dist.lower();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_uniform("boost::math::kurtosis_execess(const uniform_distribution<%1%>&)", lower, upper, &result, Policy()))
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{
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return result;
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}
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return static_cast<RealType>(-6)/5; // -6/5 = -1.2;
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} // RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist)
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template <class RealType, class Policy>
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inline RealType kurtosis(const uniform_distribution<RealType, Policy>& dist)
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{
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return kurtosis_excess(dist) + 3;
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}
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} // namespace math
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} // namespace boost
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// This include must be at the end, *after* the accessors
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// for this distribution have been defined, in order to
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// keep compilers that support two-phase lookup happy.
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#include <boost/math/distributions/detail/derived_accessors.hpp>
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#endif // BOOST_STATS_UNIFORM_HPP
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