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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_EXPONENTIAL_HPP
#define BOOST_STATS_EXPONENTIAL_HPP
#include <boost/math/distributions/fwd.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/math/special_functions/expm1.hpp>
#include <boost/math/distributions/complement.hpp>
#include <boost/math/distributions/detail/common_error_handling.hpp>
#include <boost/config/no_tr1/cmath.hpp>
#ifdef BOOST_MSVC
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
# pragma warning(disable: 4702) // unreachable code (return after domain_error throw).
#endif
#include <utility>
namespace boost{ namespace math{
namespace detail{
//
// Error check:
//
template <class RealType, class Policy>
inline bool verify_lambda(const char* function, RealType l, RealType* presult, const Policy& pol)
{
if((l <= 0) || !(boost::math::isfinite)(l))
{
*presult = policies::raise_domain_error<RealType>(
function,
"The scale parameter \"lambda\" must be > 0, but was: %1%.", l, pol);
return false;
}
return true;
}
template <class RealType, class Policy>
inline bool verify_exp_x(const char* function, RealType x, RealType* presult, const Policy& pol)
{
if((x < 0) || (boost::math::isnan)(x))
{
*presult = policies::raise_domain_error<RealType>(
function,
"The random variable must be >= 0, but was: %1%.", x, pol);
return false;
}
return true;
}
} // namespace detail
template <class RealType = double, class Policy = policies::policy<> >
class exponential_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
exponential_distribution(RealType l_lambda = 1)
: m_lambda(l_lambda)
{
RealType err;
detail::verify_lambda("boost::math::exponential_distribution<%1%>::exponential_distribution", l_lambda, &err, Policy());
} // exponential_distribution
RealType lambda()const { return m_lambda; }
private:
RealType m_lambda;
};
typedef exponential_distribution<double> exponential;
template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const exponential_distribution<RealType, Policy>& /*dist*/)
{ // Range of permissible values for random variable x.
if (std::numeric_limits<RealType>::has_infinity)
{
return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()); // 0 to + infinity.
}
else
{
using boost::math::tools::max_value;
return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max
}
}
template <class RealType, class Policy>
inline const std::pair<RealType, RealType> support(const exponential_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>());
// min_value<RealType>() to avoid a discontinuity at x = 0.
}
template <class RealType, class Policy>
inline RealType pdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::pdf(const exponential_distribution<%1%>&, %1%)";
RealType lambda = dist.lambda();
RealType result = 0;
if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
return result;
if(0 == detail::verify_exp_x(function, x, &result, Policy()))
return result;
// Workaround for VC11/12 bug:
if ((boost::math::isinf)(x))
return 0;
result = lambda * exp(-lambda * x);
return result;
} // pdf
template <class RealType, class Policy>
inline RealType cdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)";
RealType result = 0;
RealType lambda = dist.lambda();
if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
return result;
if(0 == detail::verify_exp_x(function, x, &result, Policy()))
return result;
result = -boost::math::expm1(-x * lambda, Policy());
return result;
} // cdf
template <class RealType, class Policy>
inline RealType quantile(const exponential_distribution<RealType, Policy>& dist, const RealType& p)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)";
RealType result = 0;
RealType lambda = dist.lambda();
if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
return result;
if(0 == detail::check_probability(function, p, &result, Policy()))
return result;
if(p == 0)
return 0;
if(p == 1)
return policies::raise_overflow_error<RealType>(function, 0, Policy());
result = -boost::math::log1p(-p, Policy()) / lambda;
return result;
} // quantile
template <class RealType, class Policy>
inline RealType cdf(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)";
RealType result = 0;
RealType lambda = c.dist.lambda();
if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
return result;
if(0 == detail::verify_exp_x(function, c.param, &result, Policy()))
return result;
// Workaround for VC11/12 bug:
if (c.param >= tools::max_value<RealType>())
return 0;
result = exp(-c.param * lambda);
return result;
}
template <class RealType, class Policy>
inline RealType quantile(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)";
RealType result = 0;
RealType lambda = c.dist.lambda();
if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
return result;
RealType q = c.param;
if(0 == detail::check_probability(function, q, &result, Policy()))
return result;
if(q == 1)
return 0;
if(q == 0)
return policies::raise_overflow_error<RealType>(function, 0, Policy());
result = -log(q) / lambda;
return result;
}
template <class RealType, class Policy>
inline RealType mean(const exponential_distribution<RealType, Policy>& dist)
{
RealType result = 0;
RealType lambda = dist.lambda();
if(0 == detail::verify_lambda("boost::math::mean(const exponential_distribution<%1%>&)", lambda, &result, Policy()))
return result;
return 1 / lambda;
}
template <class RealType, class Policy>
inline RealType standard_deviation(const exponential_distribution<RealType, Policy>& dist)
{
RealType result = 0;
RealType lambda = dist.lambda();
if(0 == detail::verify_lambda("boost::math::standard_deviation(const exponential_distribution<%1%>&)", lambda, &result, Policy()))
return result;
return 1 / lambda;
}
template <class RealType, class Policy>
inline RealType mode(const exponential_distribution<RealType, Policy>& /*dist*/)
{
return 0;
}
template <class RealType, class Policy>
inline RealType median(const exponential_distribution<RealType, Policy>& dist)
{
using boost::math::constants::ln_two;
return ln_two<RealType>() / dist.lambda(); // ln(2) / lambda
}
template <class RealType, class Policy>
inline RealType skewness(const exponential_distribution<RealType, Policy>& /*dist*/)
{
return 2;
}
template <class RealType, class Policy>
inline RealType kurtosis(const exponential_distribution<RealType, Policy>& /*dist*/)
{
return 9;
}
template <class RealType, class Policy>
inline RealType kurtosis_excess(const exponential_distribution<RealType, Policy>& /*dist*/)
{
return 6;
}
} // namespace math
} // namespace boost
#ifdef BOOST_MSVC
# 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_EXPONENTIAL_HPP
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