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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/weibull.hpp (12081B)

//  Copyright John Maddock 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)

#ifndef BOOST_STATS_WEIBULL_HPP
#define BOOST_STATS_WEIBULL_HPP

// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
// http://mathworld.wolfram.com/WeibullDistribution.html

#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/math/special_functions/expm1.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_weibull_shape(
      const char* function,
      RealType shape,
      RealType* result, const Policy& pol)
{
   if((shape <= 0) || !(boost::math::isfinite)(shape))
   {
      *result = policies::raise_domain_error<RealType>(
         function,
         "Shape parameter is %1%, but must be > 0 !", shape, pol);
      return false;
   }
   return true;
}

template <class RealType, class Policy>
inline bool check_weibull_x(
      const char* function,
      RealType const& x,
      RealType* result, const Policy& pol)
{
   if((x < 0) || !(boost::math::isfinite)(x))
   {
      *result = policies::raise_domain_error<RealType>(
         function,
         "Random variate is %1% but must be >= 0 !", x, pol);
      return false;
   }
   return true;
}

template <class RealType, class Policy>
inline bool check_weibull(
      const char* function,
      RealType scale,
      RealType shape,
      RealType* result, const Policy& pol)
{
   return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol);
}

} // namespace detail

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

weibull_distribution(RealType l_shape, RealType l_scale = 1)
      : m_shape(l_shape), m_scale(l_scale)
   {
      RealType result;
      detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy());
   }

RealType shape()const
   {
      return m_shape;
   }

RealType scale()const
   {
      return m_scale;
   }
private:
   //
   // Data members:
   //
   RealType m_shape;     // distribution shape
   RealType m_scale;     // distribution scale
};

typedef weibull_distribution<double> weibull;

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/)
{ // Range of permissible values for random variable x.
   using boost::math::tools::max_value;
   return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
}

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> support(const weibull_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;
   using boost::math::tools::min_value;
   return std::pair<RealType, RealType>(min_value<RealType>(),  max_value<RealType>());
   // A discontinuity at x == 0, so only support down to min_value.
}

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

static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
      return result;
   if(false == detail::check_weibull_x(function, x, &result, Policy()))
      return result;

if(x == 0)
   {
      if(shape == 1)
      {
         return 1 / scale;
      }
      if(shape > 1)
      {
         return 0;
      }
      return policies::raise_overflow_error<RealType>(function, 0, Policy());
   }
   result = exp(-pow(x / scale, shape));
   result *= pow(x / scale, shape - 1) * shape / scale;

return result;
}

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

static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

result = -boost::math::expm1(-pow(x / scale, shape), Policy());

return result;
}

template <class RealType, class Policy>
inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
      return result;
   if(false == detail::check_probability(function, p, &result, Policy()))
      return result;

if(p == 1)
      return policies::raise_overflow_error<RealType>(function, 0, Policy());

result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);

return result;
}

template <class RealType, class Policy>
inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";

RealType shape = c.dist.shape();
   RealType scale = c.dist.scale();

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
      return result;
   if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
      return result;

result = exp(-pow(c.param / scale, shape));

return result;
}

template <class RealType, class Policy>
inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";

RealType shape = c.dist.shape();
   RealType scale = c.dist.scale();
   RealType q = c.param;

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
      return result;
   if(false == detail::check_probability(function, q, &result, Policy()))
      return result;

if(q == 0)
      return policies::raise_overflow_error<RealType>(function, 0, Policy());

result = scale * pow(-log(q), 1 / shape);

return result;
}

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

static const char* function = "boost::math::mean(const weibull_distribution<%1%>)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
      return result;

result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
   return result;
}

template <class RealType, class Policy>
inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
{
   RealType shape = dist.shape();
   RealType scale = dist.scale();

static const char* function = "boost::math::variance(const weibull_distribution<%1%>)";

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
   {
      return result;
   }
   result = boost::math::tgamma(1 + 1 / shape, Policy());
   result *= -result;
   result += boost::math::tgamma(1 + 2 / shape, Policy());
   result *= scale * scale;
   return result;
}

template <class RealType, class Policy>
inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
{
   BOOST_MATH_STD_USING  // for ADL of std function pow.

static const char* function = "boost::math::mode(const weibull_distribution<%1%>)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
   {
      return result;
   }
   if(shape <= 1)
      return 0;
   result = scale * pow((shape - 1) / shape, 1 / shape);
   return result;
}

template <class RealType, class Policy>
inline RealType median(const weibull_distribution<RealType, Policy>& dist)
{
   BOOST_MATH_STD_USING  // for ADL of std function pow.

static const char* function = "boost::math::median(const weibull_distribution<%1%>)";

RealType shape = dist.shape(); // Wikipedia k
   RealType scale = dist.scale(); // Wikipedia lambda

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
   {
      return result;
   }
   using boost::math::constants::ln_two;
   result = scale * pow(ln_two<RealType>(), 1 / shape);
   return result;
}

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

static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
   {
      return result;
   }
   RealType g1, g2, g3, d;

g1 = boost::math::tgamma(1 + 1 / shape, Policy());
   g2 = boost::math::tgamma(1 + 2 / shape, Policy());
   g3 = boost::math::tgamma(1 + 3 / shape, Policy());
   d = pow(g2 - g1 * g1, RealType(1.5));

result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
   return result;
}

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

static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
      return result;

RealType g1, g2, g3, g4, d, g1_2, g1_4;

g1 = boost::math::tgamma(1 + 1 / shape, Policy());
   g2 = boost::math::tgamma(1 + 2 / shape, Policy());
   g3 = boost::math::tgamma(1 + 3 / shape, Policy());
   g4 = boost::math::tgamma(1 + 4 / shape, Policy());
   g1_2 = g1 * g1;
   g1_4 = g1_2 * g1_2;
   d = g2 - g1_2;
   d *= d;

result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
   result /= d;
   return result;
}

template <class RealType, class Policy>
inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
{
   return kurtosis_excess(dist) + 3;
}

template <class RealType, class Policy>
inline RealType entropy(const weibull_distribution<RealType, Policy>& dist)
{
   using std::log;
   RealType k = dist.shape();
   RealType lambda = dist.scale();
   return constants::euler<RealType>()*(1-1/k) + log(lambda/k) + 1;
}

} // 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_WEIBULL_HPP

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