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// 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_DERIVED_HPP
#define BOOST_STATS_DERIVED_HPP
// This file implements various common properties of distributions
// that can be implemented in terms of other properties:
// variance OR standard deviation (see note below),
// hazard, cumulative hazard (chf), coefficient_of_variation.
//
// Note that while both variance and standard_deviation are provided
// here, each distribution MUST SPECIALIZE AT LEAST ONE OF THESE
// otherwise these two versions will just call each other over and over
// until stack space runs out ...
// Of course there may be more efficient means of implementing these
// that are specific to a particular distribution, but these generic
// versions give these properties "for free" with most distributions.
//
// In order to make use of this header, it must be included AT THE END
// of the distribution header, AFTER the distribution and its core
// property accessors have been defined: this is so that compilers
// that implement 2-phase lookup and early-type-checking of templates
// can find the definitions refered to herein.
//
#include <boost/type_traits/is_same.hpp>
#include <boost/static_assert.hpp>
#ifdef BOOST_MSVC
# pragma warning(push)
# pragma warning(disable: 4723) // potential divide by 0
// Suppressing spurious warning in coefficient_of_variation
#endif
namespace boost{ namespace math{
template <class Distribution>
typename Distribution::value_type variance(const Distribution& dist);
template <class Distribution>
inline typename Distribution::value_type standard_deviation(const Distribution& dist)
{
BOOST_MATH_STD_USING // ADL of sqrt.
return sqrt(variance(dist));
}
template <class Distribution>
inline typename Distribution::value_type variance(const Distribution& dist)
{
typename Distribution::value_type result = standard_deviation(dist);
return result * result;
}
template <class Distribution, class RealType>
inline typename Distribution::value_type hazard(const Distribution& dist, const RealType& x)
{ // hazard function
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm#HAZ
typedef typename Distribution::value_type value_type;
typedef typename Distribution::policy_type policy_type;
value_type p = cdf(complement(dist, x));
value_type d = pdf(dist, x);
if(d > p * tools::max_value<value_type>())
return policies::raise_overflow_error<value_type>(
"boost::math::hazard(const Distribution&, %1%)", 0, policy_type());
if(d == 0)
{
// This protects against 0/0, but is it the right thing to do?
return 0;
}
return d / p;
}
template <class Distribution, class RealType>
inline typename Distribution::value_type chf(const Distribution& dist, const RealType& x)
{ // cumulative hazard function.
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm#HAZ
BOOST_MATH_STD_USING
return -log(cdf(complement(dist, x)));
}
template <class Distribution>
inline typename Distribution::value_type coefficient_of_variation(const Distribution& dist)
{
typedef typename Distribution::value_type value_type;
typedef typename Distribution::policy_type policy_type;
using std::abs;
value_type m = mean(dist);
value_type d = standard_deviation(dist);
if((abs(m) < 1) && (d > abs(m) * tools::max_value<value_type>()))
{ // Checks too that m is not zero,
return policies::raise_overflow_error<value_type>("boost::math::coefficient_of_variation(const Distribution&, %1%)", 0, policy_type());
}
return d / m; // so MSVC warning on zerodivide is spurious, and suppressed.
}
//
// Next follow overloads of some of the standard accessors with mixed
// argument types. We just use a typecast to forward on to the "real"
// implementation with all arguments of the same type:
//
template <class Distribution, class RealType>
inline typename Distribution::value_type pdf(const Distribution& dist, const RealType& x)
{
typedef typename Distribution::value_type value_type;
return pdf(dist, static_cast<value_type>(x));
}
template <class Distribution, class RealType>
inline typename Distribution::value_type cdf(const Distribution& dist, const RealType& x)
{
typedef typename Distribution::value_type value_type;
return cdf(dist, static_cast<value_type>(x));
}
template <class Distribution, class RealType>
inline typename Distribution::value_type quantile(const Distribution& dist, const RealType& x)
{
typedef typename Distribution::value_type value_type;
return quantile(dist, static_cast<value_type>(x));
}
/*
template <class Distribution, class RealType>
inline typename Distribution::value_type chf(const Distribution& dist, const RealType& x)
{
typedef typename Distribution::value_type value_type;
return chf(dist, static_cast<value_type>(x));
}
*/
template <class Distribution, class RealType>
inline typename Distribution::value_type cdf(const complemented2_type<Distribution, RealType>& c)
{
typedef typename Distribution::value_type value_type;
return cdf(complement(c.dist, static_cast<value_type>(c.param)));
}
template <class Distribution, class RealType>
inline typename Distribution::value_type quantile(const complemented2_type<Distribution, RealType>& c)
{
typedef typename Distribution::value_type value_type;
return quantile(complement(c.dist, static_cast<value_type>(c.param)));
}
template <class Dist>
inline typename Dist::value_type median(const Dist& d)
{ // median - default definition for those distributions for which a
// simple closed form is not known,
// and for which a domain_error and/or NaN generating function is NOT defined.
typedef typename Dist::value_type value_type;
return quantile(d, static_cast<value_type>(0.5f));
}
} // namespace math
} // namespace boost
#ifdef BOOST_MSVC
# pragma warning(pop)
#endif
#endif // BOOST_STATS_DERIVED_HPP
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