363 lines
12 KiB
Plaintext
363 lines
12 KiB
Plaintext
// Copyright John Maddock 2006, 2007.
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// Copyright Paul A. Bristow 2007.
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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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#ifndef BOOST_STATS_CAUCHY_HPP
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#define BOOST_STATS_CAUCHY_HPP
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#ifdef _MSC_VER
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#pragma warning(push)
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#pragma warning(disable : 4127) // conditional expression is constant
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#endif
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/distributions/complement.hpp>
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#include <boost/math/distributions/detail/common_error_handling.hpp>
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#include <boost/config/no_tr1/cmath.hpp>
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#include <utility>
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namespace boost{ namespace math
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{
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template <class RealType, class Policy>
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class cauchy_distribution;
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namespace detail
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{
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template <class RealType, class Policy>
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RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement)
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{
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//
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// This calculates the cdf of the Cauchy distribution and/or its complement.
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//
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// The usual formula for the Cauchy cdf is:
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//
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// cdf = 0.5 + atan(x)/pi
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//
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// But that suffers from cancellation error as x -> -INF.
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//
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// Recall that for x < 0:
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//
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// atan(x) = -pi/2 - atan(1/x)
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//
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// Substituting into the above we get:
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//
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// CDF = -atan(1/x) ; x < 0
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//
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// So the proceedure is to calculate the cdf for -fabs(x)
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// using the above formula, and then subtract from 1 when required
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// to get the result.
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//
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::cdf(cauchy<%1%>&, %1%)";
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RealType result = 0;
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RealType location = dist.location();
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RealType scale = dist.scale();
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if(false == detail::check_location(function, location, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_scale(function, scale, &result, Policy()))
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{
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return result;
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}
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if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
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{ // cdf +infinity is unity.
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return static_cast<RealType>((complement) ? 0 : 1);
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}
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if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
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{ // cdf -infinity is zero.
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return static_cast<RealType>((complement) ? 1 : 0);
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}
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if(false == detail::check_x(function, x, &result, Policy()))
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{ // Catches x == NaN
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return result;
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}
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RealType mx = -fabs((x - location) / scale); // scale is > 0
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if(mx > -tools::epsilon<RealType>() / 8)
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{ // special case first: x extremely close to location.
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return 0.5;
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}
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result = -atan(1 / mx) / constants::pi<RealType>();
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return (((x > location) != complement) ? 1 - result : result);
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} // cdf
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template <class RealType, class Policy>
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RealType quantile_imp(
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const cauchy_distribution<RealType, Policy>& dist,
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const RealType& p,
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bool complement)
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{
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// This routine implements the quantile for the Cauchy distribution,
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// the value p may be the probability, or its complement if complement=true.
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//
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// The procedure first performs argument reduction on p to avoid error
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// when calculating the tangent, then calulates the distance from the
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// mid-point of the distribution. This is either added or subtracted
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// from the location parameter depending on whether `complement` is true.
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//
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static const char* function = "boost::math::quantile(cauchy<%1%>&, %1%)";
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BOOST_MATH_STD_USING // for ADL of std functions
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RealType result = 0;
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RealType location = dist.location();
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RealType scale = dist.scale();
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if(false == detail::check_location(function, location, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_scale(function, scale, &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(function, p, &result, Policy()))
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{
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return result;
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}
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// Special cases:
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if(p == 1)
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{
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return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
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}
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if(p == 0)
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{
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return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
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}
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RealType P = p - floor(p); // argument reduction of p:
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if(P > 0.5)
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{
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P = P - 1;
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}
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if(P == 0.5) // special case:
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{
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return location;
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}
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result = -scale / tan(constants::pi<RealType>() * P);
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return complement ? RealType(location - result) : RealType(location + result);
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} // quantile
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} // namespace detail
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template <class RealType = double, class Policy = policies::policy<> >
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class cauchy_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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cauchy_distribution(RealType l_location = 0, RealType l_scale = 1)
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: m_a(l_location), m_hg(l_scale)
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{
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static const char* function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution";
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RealType result;
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detail::check_location(function, l_location, &result, Policy());
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detail::check_scale(function, l_scale, &result, Policy());
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} // cauchy_distribution
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RealType location()const
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{
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return m_a;
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}
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RealType scale()const
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{
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return m_hg;
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}
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private:
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RealType m_a; // The location, this is the median of the distribution.
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RealType m_hg; // The scale )or shape), this is the half width at half height.
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};
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typedef cauchy_distribution<double> cauchy;
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&)
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{ // Range of permissible values for random variable x.
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if (std::numeric_limits<RealType>::has_infinity)
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{
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return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
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}
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else
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{ // Can only use max_value.
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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 + max.
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}
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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 cauchy_distribution<RealType, Policy>& )
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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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if (std::numeric_limits<RealType>::has_infinity)
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{
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return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
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}
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else
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{ // Can only use max_value.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max.
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}
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}
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template <class RealType, class Policy>
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inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::pdf(cauchy<%1%>&, %1%)";
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RealType result = 0;
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RealType location = dist.location();
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RealType scale = dist.scale();
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if(false == detail::check_scale("boost::math::pdf(cauchy<%1%>&, %1%)", scale, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_location("boost::math::pdf(cauchy<%1%>&, %1%)", location, &result, Policy()))
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{
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return result;
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}
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if((boost::math::isinf)(x))
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{
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return 0; // pdf + and - infinity is zero.
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}
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// These produce MSVC 4127 warnings, so the above used instead.
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//if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
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//{ // pdf + and - infinity is zero.
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// return 0;
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//}
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if(false == detail::check_x(function, x, &result, Policy()))
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{ // Catches x = NaN
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return result;
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}
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RealType xs = (x - location) / scale;
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result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs));
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return result;
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} // pdf
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template <class RealType, class Policy>
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inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
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{
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return detail::cdf_imp(dist, x, false);
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} // cdf
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template <class RealType, class Policy>
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inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p)
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{
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return detail::quantile_imp(dist, p, false);
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} // quantile
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
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{
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return detail::cdf_imp(c.dist, c.param, true);
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} // cdf complement
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template <class RealType, class Policy>
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inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
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{
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return detail::quantile_imp(c.dist, c.param, true);
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} // quantile complement
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template <class RealType, class Policy>
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inline RealType mean(const cauchy_distribution<RealType, Policy>&)
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{ // There is no mean:
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typedef typename Policy::assert_undefined_type assert_type;
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BOOST_STATIC_ASSERT(assert_type::value == 0);
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return policies::raise_domain_error<RealType>(
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"boost::math::mean(cauchy<%1%>&)",
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"The Cauchy distribution does not have a mean: "
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"the only possible return value is %1%.",
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std::numeric_limits<RealType>::quiet_NaN(), Policy());
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}
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template <class RealType, class Policy>
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inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/)
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{
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// There is no variance:
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typedef typename Policy::assert_undefined_type assert_type;
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BOOST_STATIC_ASSERT(assert_type::value == 0);
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return policies::raise_domain_error<RealType>(
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"boost::math::variance(cauchy<%1%>&)",
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"The Cauchy distribution does not have a variance: "
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"the only possible return value is %1%.",
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std::numeric_limits<RealType>::quiet_NaN(), Policy());
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}
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template <class RealType, class Policy>
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inline RealType mode(const cauchy_distribution<RealType, Policy>& dist)
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{
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return dist.location();
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}
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template <class RealType, class Policy>
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inline RealType median(const cauchy_distribution<RealType, Policy>& dist)
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{
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return dist.location();
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}
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template <class RealType, class Policy>
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inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/)
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{
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// There is no skewness:
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typedef typename Policy::assert_undefined_type assert_type;
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BOOST_STATIC_ASSERT(assert_type::value == 0);
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return policies::raise_domain_error<RealType>(
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"boost::math::skewness(cauchy<%1%>&)",
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"The Cauchy distribution does not have a skewness: "
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"the only possible return value is %1%.",
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std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?
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}
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template <class RealType, class Policy>
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inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/)
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{
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// There is no kurtosis:
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typedef typename Policy::assert_undefined_type assert_type;
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BOOST_STATIC_ASSERT(assert_type::value == 0);
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return policies::raise_domain_error<RealType>(
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"boost::math::kurtosis(cauchy<%1%>&)",
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"The Cauchy distribution does not have a kurtosis: "
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"the only possible return value is %1%.",
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std::numeric_limits<RealType>::quiet_NaN(), Policy());
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/)
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{
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// There is no kurtosis excess:
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typedef typename Policy::assert_undefined_type assert_type;
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BOOST_STATIC_ASSERT(assert_type::value == 0);
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return policies::raise_domain_error<RealType>(
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"boost::math::kurtosis_excess(cauchy<%1%>&)",
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"The Cauchy distribution does not have a kurtosis: "
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"the only possible return value is %1%.",
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std::numeric_limits<RealType>::quiet_NaN(), Policy());
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}
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} // namespace math
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} // namespace boost
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#ifdef _MSC_VER
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#pragma warning(pop)
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#endif
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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_CAUCHY_HPP
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