Chris@16: // Copyright John Maddock 2006, 2007.
Chris@16: // Copyright Paul A. Bristow 2007.
Chris@16: 
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_STATS_CAUCHY_HPP
Chris@16: #define BOOST_STATS_CAUCHY_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma warning(push)
Chris@16: #pragma warning(disable : 4127) // conditional expression is constant
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/constants/constants.hpp>
Chris@16: #include <boost/math/distributions/complement.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: #include <boost/config/no_tr1/cmath.hpp>
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: namespace boost{ namespace math
Chris@16: {
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: class cauchy_distribution;
Chris@16: 
Chris@16: namespace detail
Chris@16: {
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement)
Chris@16: {
Chris@16:    //
Chris@16:    // This calculates the cdf of the Cauchy distribution and/or its complement.
Chris@16:    //
Chris@16:    // The usual formula for the Cauchy cdf is:
Chris@16:    //
Chris@16:    // cdf = 0.5 + atan(x)/pi
Chris@16:    //
Chris@16:    // But that suffers from cancellation error as x -> -INF.
Chris@16:    //
Chris@16:    // Recall that for x < 0:
Chris@16:    //
Chris@16:    // atan(x) = -pi/2 - atan(1/x)
Chris@16:    //
Chris@16:    // Substituting into the above we get:
Chris@16:    //
Chris@16:    // CDF = -atan(1/x)  ; x < 0
Chris@16:    //
Chris@16:    // So the proceedure is to calculate the cdf for -fabs(x)
Chris@16:    // using the above formula, and then subtract from 1 when required
Chris@16:    // to get the result.
Chris@16:    //
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16:    static const char* function = "boost::math::cdf(cauchy<%1%>&, %1%)";
Chris@16:    RealType result = 0;
Chris@16:    RealType location = dist.location();
Chris@16:    RealType scale = dist.scale();
Chris@16:    if(false == detail::check_location(function, location, &result, Policy()))
Chris@16:    {
Chris@16:      return result;
Chris@16:    }
Chris@16:    if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
Chris@16:    { // cdf +infinity is unity.
Chris@16:      return static_cast<RealType>((complement) ? 0 : 1);
Chris@16:    }
Chris@16:    if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
Chris@16:    { // cdf -infinity is zero.
Chris@16:      return static_cast<RealType>((complement) ? 1 : 0);
Chris@16:    }
Chris@16:    if(false == detail::check_x(function, x, &result, Policy()))
Chris@16:    { // Catches x == NaN
Chris@16:       return result;
Chris@16:    }
Chris@16:    RealType mx = -fabs((x - location) / scale); // scale is > 0
Chris@16:    if(mx > -tools::epsilon<RealType>() / 8)
Chris@16:    {  // special case first: x extremely close to location.
Chris@16:       return 0.5;
Chris@16:    }
Chris@16:    result = -atan(1 / mx) / constants::pi<RealType>();
Chris@16:    return (((x > location) != complement) ? 1 - result : result);
Chris@16: } // cdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: RealType quantile_imp(
Chris@16:       const cauchy_distribution<RealType, Policy>& dist,
Chris@16:       const RealType& p,
Chris@16:       bool complement)
Chris@16: {
Chris@16:    // This routine implements the quantile for the Cauchy distribution,
Chris@16:    // the value p may be the probability, or its complement if complement=true.
Chris@16:    //
Chris@16:    // The procedure first performs argument reduction on p to avoid error
Chris@16:    // when calculating the tangent, then calulates the distance from the
Chris@16:    // mid-point of the distribution.  This is either added or subtracted
Chris@16:    // from the location parameter depending on whether `complement` is true.
Chris@16:    //
Chris@16:    static const char* function = "boost::math::quantile(cauchy<%1%>&, %1%)";
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    RealType location = dist.location();
Chris@16:    RealType scale = dist.scale();
Chris@16:    if(false == detail::check_location(function, location, &result, Policy()))
Chris@16:    {
Chris@16:      return result;
Chris@16:    }
Chris@16:    if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if(false == detail::check_probability(function, p, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    // Special cases:
Chris@16:    if(p == 1)
Chris@16:    {
Chris@16:       return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    }
Chris@16:    if(p == 0)
Chris@16:    {
Chris@16:       return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    }
Chris@16: 
Chris@16:    RealType P = p - floor(p);   // argument reduction of p:
Chris@16:    if(P > 0.5)
Chris@16:    {
Chris@16:       P = P - 1;
Chris@16:    }
Chris@16:    if(P == 0.5)   // special case:
Chris@16:    {
Chris@16:       return location;
Chris@16:    }
Chris@16:    result = -scale / tan(constants::pi<RealType>() * P);
Chris@16:    return complement ? RealType(location - result) : RealType(location + result);
Chris@16: } // quantile
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class cauchy_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    cauchy_distribution(RealType l_location = 0, RealType l_scale = 1)
Chris@16:       : m_a(l_location), m_hg(l_scale)
Chris@16:    {
Chris@16:     static const char* function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution";
Chris@16:      RealType result;
Chris@16:      detail::check_location(function, l_location, &result, Policy());
Chris@16:      detail::check_scale(function, l_scale, &result, Policy());
Chris@16:    } // cauchy_distribution
Chris@16: 
Chris@16:    RealType location()const
Chris@16:    {
Chris@16:       return m_a;
Chris@16:    }
Chris@16:    RealType scale()const
Chris@16:    {
Chris@16:       return m_hg;
Chris@16:    }
Chris@16: 
Chris@16: private:
Chris@16:    RealType m_a;    // The location, this is the median of the distribution.
Chris@16:    RealType m_hg;   // The scale )or shape), this is the half width at half height.
Chris@16: };
Chris@16: 
Chris@16: typedef cauchy_distribution<double> cauchy;
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&)
Chris@16: { // Range of permissible values for random variable x.
Chris@16:   if (std::numeric_limits<RealType>::has_infinity)
Chris@16:   { 
Chris@16:      return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
Chris@16:   }
Chris@16:   else
Chris@16:   { // Can only use max_value.
Chris@16:    using boost::math::tools::max_value;
Chris@16:    return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max.
Chris@16:   }
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> support(const cauchy_distribution<RealType, Policy>& )
Chris@16: { // Range of supported values for random variable x.
Chris@16:    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@16:   if (std::numeric_limits<RealType>::has_infinity)
Chris@16:   { 
Chris@16:      return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
Chris@16:   }
Chris@16:   else
Chris@16:   { // Can only use max_value.
Chris@16:      using boost::math::tools::max_value;
Chris@16:      return std::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max.
Chris@16:   }
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {  
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::pdf(cauchy<%1%>&, %1%)";
Chris@16:    RealType result = 0;
Chris@16:    RealType location = dist.location();
Chris@16:    RealType scale = dist.scale();
Chris@16:    if(false == detail::check_scale("boost::math::pdf(cauchy<%1%>&, %1%)", scale, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if(false == detail::check_location("boost::math::pdf(cauchy<%1%>&, %1%)", location, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if((boost::math::isinf)(x))
Chris@16:    {
Chris@16:      return 0; // pdf + and - infinity is zero.
Chris@16:    }
Chris@16:    // These produce MSVC 4127 warnings, so the above used instead.
Chris@16:    //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
Chris@16:    //{ // pdf + and - infinity is zero.
Chris@16:    //  return 0;
Chris@16:    //}
Chris@16: 
Chris@16:    if(false == detail::check_x(function, x, &result, Policy()))
Chris@16:    { // Catches x = NaN
Chris@16:       return result;
Chris@16:    }
Chris@16: 
Chris@16:    RealType xs = (x - location) / scale;
Chris@16:    result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs));
Chris@16:    return result;
Chris@16: } // pdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    return detail::cdf_imp(dist, x, false);
Chris@16: } // cdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    return detail::quantile_imp(dist, p, false);
Chris@16: } // quantile
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    return detail::cdf_imp(c.dist, c.param, true);
Chris@16: } //  cdf complement
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    return detail::quantile_imp(c.dist, c.param, true);
Chris@16: } // quantile complement
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const cauchy_distribution<RealType, Policy>&)
Chris@16: {  // There is no mean:
Chris@16:    typedef typename Policy::assert_undefined_type assert_type;
Chris@16:    BOOST_STATIC_ASSERT(assert_type::value == 0);
Chris@16: 
Chris@16:    return policies::raise_domain_error<RealType>(
Chris@16:       "boost::math::mean(cauchy<%1%>&)",
Chris@16:       "The Cauchy distribution does not have a mean: "
Chris@16:       "the only possible return value is %1%.",
Chris@16:       std::numeric_limits<RealType>::quiet_NaN(), Policy());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    // There is no variance:
Chris@16:    typedef typename Policy::assert_undefined_type assert_type;
Chris@16:    BOOST_STATIC_ASSERT(assert_type::value == 0);
Chris@16: 
Chris@16:    return policies::raise_domain_error<RealType>(
Chris@16:       "boost::math::variance(cauchy<%1%>&)",
Chris@16:       "The Cauchy distribution does not have a variance: "
Chris@16:       "the only possible return value is %1%.",
Chris@16:       std::numeric_limits<RealType>::quiet_NaN(), Policy());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const cauchy_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return dist.location();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType median(const cauchy_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return dist.location();
Chris@16: }
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    // There is no skewness:
Chris@16:    typedef typename Policy::assert_undefined_type assert_type;
Chris@16:    BOOST_STATIC_ASSERT(assert_type::value == 0);
Chris@16: 
Chris@16:    return policies::raise_domain_error<RealType>(
Chris@16:       "boost::math::skewness(cauchy<%1%>&)",
Chris@16:       "The Cauchy distribution does not have a skewness: "
Chris@16:       "the only possible return value is %1%.",
Chris@16:       std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    // There is no kurtosis:
Chris@16:    typedef typename Policy::assert_undefined_type assert_type;
Chris@16:    BOOST_STATIC_ASSERT(assert_type::value == 0);
Chris@16: 
Chris@16:    return policies::raise_domain_error<RealType>(
Chris@16:       "boost::math::kurtosis(cauchy<%1%>&)",
Chris@16:       "The Cauchy distribution does not have a kurtosis: "
Chris@16:       "the only possible return value is %1%.",
Chris@16:       std::numeric_limits<RealType>::quiet_NaN(), Policy());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:    // There is no kurtosis excess:
Chris@16:    typedef typename Policy::assert_undefined_type assert_type;
Chris@16:    BOOST_STATIC_ASSERT(assert_type::value == 0);
Chris@16: 
Chris@16:    return policies::raise_domain_error<RealType>(
Chris@16:       "boost::math::kurtosis_excess(cauchy<%1%>&)",
Chris@16:       "The Cauchy distribution does not have a kurtosis: "
Chris@16:       "the only possible return value is %1%.",
Chris@16:       std::numeric_limits<RealType>::quiet_NaN(), Policy());
Chris@16: }
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: // This include must be at the end, *after* the accessors
Chris@16: // for this distribution have been defined, in order to
Chris@16: // keep compilers that support two-phase lookup happy.
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #endif // BOOST_STATS_CAUCHY_HPP