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/usr/include/boost/math/distributions

Name	Size	Mode	Actions
detail/	-	0755	rm
arcsine.hpp	18797	0644	edit dl rm
bernoulli.hpp	12143	0644	edit dl rm
beta.hpp	18807	0644	edit dl rm
binomial.hpp	28654	0644	edit dl rm
cauchy.hpp	12310	0644	edit dl rm
chi_squared.hpp	12242	0644	edit dl rm
complement.hpp	5978	0644	edit dl rm
empirical_cumulative_distribution_function.hpp	1886	0644	edit dl rm
exponential.hpp	8944	0644	edit dl rm
extreme_value.hpp	10491	0644	edit dl rm
find_location.hpp	6713	0644	edit dl rm
find_scale.hpp	9674	0644	edit dl rm
fisher_f.hpp	14391	0644	edit dl rm
fwd.hpp	5461	0644	edit dl rm
gamma.hpp	10660	0644	edit dl rm
geometric.hpp	21156	0644	edit dl rm
hyperexponential.hpp	21887	0644	edit dl rm
hypergeometric.hpp	12220	0644	edit dl rm
inverse_chi_squared.hpp	15202	0644	edit dl rm
inverse_gamma.hpp	15389	0644	edit dl rm
inverse_gaussian.hpp	19760	0644	edit dl rm
laplace.hpp	10580	0644	edit dl rm
logistic.hpp	11273	0644	edit dl rm
lognormal.hpp	11714	0644	edit dl rm
negative_binomial.hpp	26139	0644	edit dl rm
non_central_beta.hpp	35837	0644	edit dl rm
non_central_chi_squared.hpp	40704	0644	edit dl rm
non_central_f.hpp	15848	0644	edit dl rm
non_central_t.hpp	47973	0644	edit dl rm
normal.hpp	10768	0644	edit dl rm
pareto.hpp	15516	0644	edit dl rm
poisson.hpp	20267	0644	edit dl rm
rayleigh.hpp	10344	0644	edit dl rm
skew_normal.hpp	25646	0644	edit dl rm
students_t.hpp	18476	0644	edit dl rm
triangular.hpp	18407	0644	edit dl rm
uniform.hpp	12963	0644	edit dl rm
weibull.hpp	12081	0644	edit dl rm

Edit: /usr/include/boost/math/distributions/cauchy.hpp (12310B)

// Copyright John Maddock 2006, 2007.
// Copyright Paul A. Bristow 2007.

//  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)

#ifndef BOOST_STATS_CAUCHY_HPP
#define BOOST_STATS_CAUCHY_HPP

#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable : 4127) // conditional expression is constant
#endif

#include <boost/math/distributions/fwd.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/distributions/complement.hpp>
#include <boost/math/distributions/detail/common_error_handling.hpp>
#include <boost/config/no_tr1/cmath.hpp>

#include <utility>

namespace boost{ namespace math
{

template <class RealType, class Policy>
class cauchy_distribution;

namespace detail
{

template <class RealType, class Policy>
RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement)
{
   //
   // This calculates the cdf of the Cauchy distribution and/or its complement.
   //
   // The usual formula for the Cauchy cdf is:
   //
   // cdf = 0.5 + atan(x)/pi
   //
   // But that suffers from cancellation error as x -> -INF.
   //
   // Recall that for x < 0:
   //
   // atan(x) = -pi/2 - atan(1/x)
   //
   // Substituting into the above we get:
   //
   // CDF = -atan(1/x)  ; x < 0
   //
   // So the procedure is to calculate the cdf for -fabs(x)
   // using the above formula, and then subtract from 1 when required
   // to get the result.
   //
   BOOST_MATH_STD_USING // for ADL of std functions
   static const char* function = "boost::math::cdf(cauchy<%1%>&, %1%)";
   RealType result = 0;
   RealType location = dist.location();
   RealType scale = dist.scale();
   if(false == detail::check_location(function, location, &result, Policy()))
   {
     return result;
   }
   if(false == detail::check_scale(function, scale, &result, Policy()))
   {
      return result;
   }
   if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
   { // cdf +infinity is unity.
     return static_cast<RealType>((complement) ? 0 : 1);
   }
   if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
   { // cdf -infinity is zero.
     return static_cast<RealType>((complement) ? 1 : 0);
   }
   if(false == detail::check_x(function, x, &result, Policy()))
   { // Catches x == NaN
      return result;
   }
   RealType mx = -fabs((x - location) / scale); // scale is > 0
   if(mx > -tools::epsilon<RealType>() / 8)
   {  // special case first: x extremely close to location.
      return 0.5;
   }
   result = -atan(1 / mx) / constants::pi<RealType>();
   return (((x > location) != complement) ? 1 - result : result);
} // cdf

template <class RealType, class Policy>
RealType quantile_imp(
      const cauchy_distribution<RealType, Policy>& dist,
      const RealType& p,
      bool complement)
{
   // This routine implements the quantile for the Cauchy distribution,
   // the value p may be the probability, or its complement if complement=true.
   //
   // The procedure first performs argument reduction on p to avoid error
   // when calculating the tangent, then calculates the distance from the
   // mid-point of the distribution.  This is either added or subtracted
   // from the location parameter depending on whether `complement` is true.
   //
   static const char* function = "boost::math::quantile(cauchy<%1%>&, %1%)";
   BOOST_MATH_STD_USING // for ADL of std functions

RealType result = 0;
   RealType location = dist.location();
   RealType scale = dist.scale();
   if(false == detail::check_location(function, location, &result, Policy()))
   {
     return result;
   }
   if(false == detail::check_scale(function, scale, &result, Policy()))
   {
      return result;
   }
   if(false == detail::check_probability(function, p, &result, Policy()))
   {
      return result;
   }
   // Special cases:
   if(p == 1)
   {
      return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
   }
   if(p == 0)
   {
      return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
   }

RealType P = p - floor(p);   // argument reduction of p:
   if(P > 0.5)
   {
      P = P - 1;
   }
   if(P == 0.5)   // special case:
   {
      return location;
   }
   result = -scale / tan(constants::pi<RealType>() * P);
   return complement ? RealType(location - result) : RealType(location + result);
} // quantile

} // namespace detail

template <class RealType = double, class Policy = policies::policy<> >
class cauchy_distribution
{
public:
   typedef RealType value_type;
   typedef Policy policy_type;

cauchy_distribution(RealType l_location = 0, RealType l_scale = 1)
      : m_a(l_location), m_hg(l_scale)
   {
    static const char* function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution";
     RealType result;
     detail::check_location(function, l_location, &result, Policy());
     detail::check_scale(function, l_scale, &result, Policy());
   } // cauchy_distribution

RealType location()const
   {
      return m_a;
   }
   RealType scale()const
   {
      return m_hg;
   }

private:
   RealType m_a;    // The location, this is the median of the distribution.
   RealType m_hg;   // The scale )or shape), this is the half width at half height.
};

typedef cauchy_distribution<double> cauchy;

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&)
{ // Range of permissible values for random variable x.
  if (std::numeric_limits<RealType>::has_infinity)
  { 
     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
  }
  else
  { // Can only use max_value.
   using boost::math::tools::max_value;
   return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max.
  }
}

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> support(const cauchy_distribution<RealType, Policy>& )
{ // 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.
  if (std::numeric_limits<RealType>::has_infinity)
  { 
     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
  }
  else
  { // Can only use max_value.
     using boost::math::tools::max_value;
     return std::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max.
  }
}

template <class RealType, class Policy>
inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
{  
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::pdf(cauchy<%1%>&, %1%)";
   RealType result = 0;
   RealType location = dist.location();
   RealType scale = dist.scale();
   if(false == detail::check_scale("boost::math::pdf(cauchy<%1%>&, %1%)", scale, &result, Policy()))
   {
      return result;
   }
   if(false == detail::check_location("boost::math::pdf(cauchy<%1%>&, %1%)", location, &result, Policy()))
   {
      return result;
   }
   if((boost::math::isinf)(x))
   {
     return 0; // pdf + and - infinity is zero.
   }
   // These produce MSVC 4127 warnings, so the above used instead.
   //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
   //{ // pdf + and - infinity is zero.
   //  return 0;
   //}

if(false == detail::check_x(function, x, &result, Policy()))
   { // Catches x = NaN
      return result;
   }

RealType xs = (x - location) / scale;
   result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs));
   return result;
} // pdf

template <class RealType, class Policy>
inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
{
   return detail::cdf_imp(dist, x, false);
} // cdf

template <class RealType, class Policy>
inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p)
{
   return detail::quantile_imp(dist, p, false);
} // quantile

template <class RealType, class Policy>
inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
{
   return detail::cdf_imp(c.dist, c.param, true);
} //  cdf complement

template <class RealType, class Policy>
inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
{
   return detail::quantile_imp(c.dist, c.param, true);
} // quantile complement

template <class RealType, class Policy>
inline RealType mean(const cauchy_distribution<RealType, Policy>&)
{  // There is no mean:
   typedef typename Policy::assert_undefined_type assert_type;
   BOOST_STATIC_ASSERT(assert_type::value == 0);

return policies::raise_domain_error<RealType>(
      "boost::math::mean(cauchy<%1%>&)",
      "The Cauchy distribution does not have a mean: "
      "the only possible return value is %1%.",
      std::numeric_limits<RealType>::quiet_NaN(), Policy());
}

template <class RealType, class Policy>
inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/)
{
   // There is no variance:
   typedef typename Policy::assert_undefined_type assert_type;
   BOOST_STATIC_ASSERT(assert_type::value == 0);

return policies::raise_domain_error<RealType>(
      "boost::math::variance(cauchy<%1%>&)",
      "The Cauchy distribution does not have a variance: "
      "the only possible return value is %1%.",
      std::numeric_limits<RealType>::quiet_NaN(), Policy());
}

template <class RealType, class Policy>
inline RealType mode(const cauchy_distribution<RealType, Policy>& dist)
{
   return dist.location();
}

template <class RealType, class Policy>
inline RealType median(const cauchy_distribution<RealType, Policy>& dist)
{
   return dist.location();
}
template <class RealType, class Policy>
inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/)
{
   // There is no skewness:
   typedef typename Policy::assert_undefined_type assert_type;
   BOOST_STATIC_ASSERT(assert_type::value == 0);

return policies::raise_domain_error<RealType>(
      "boost::math::skewness(cauchy<%1%>&)",
      "The Cauchy distribution does not have a skewness: "
      "the only possible return value is %1%.",
      std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?
}

template <class RealType, class Policy>
inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/)
{
   // There is no kurtosis:
   typedef typename Policy::assert_undefined_type assert_type;
   BOOST_STATIC_ASSERT(assert_type::value == 0);

return policies::raise_domain_error<RealType>(
      "boost::math::kurtosis(cauchy<%1%>&)",
      "The Cauchy distribution does not have a kurtosis: "
      "the only possible return value is %1%.",
      std::numeric_limits<RealType>::quiet_NaN(), Policy());
}

template <class RealType, class Policy>
inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/)
{
   // There is no kurtosis excess:
   typedef typename Policy::assert_undefined_type assert_type;
   BOOST_STATIC_ASSERT(assert_type::value == 0);

return policies::raise_domain_error<RealType>(
      "boost::math::kurtosis_excess(cauchy<%1%>&)",
      "The Cauchy distribution does not have a kurtosis: "
      "the only possible return value is %1%.",
      std::numeric_limits<RealType>::quiet_NaN(), Policy());
}

template <class RealType, class Policy>
inline RealType entropy(const cauchy_distribution<RealType, Policy> & dist)
{
   using std::log;
   return log(2*constants::two_pi<RealType>()*dist.scale());
}

} // namespace math
} // namespace boost

#ifdef _MSC_VER
#pragma warning(pop)
#endif

// 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_CAUCHY_HPP

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