math/distributions/exponential.hpp

0001 //  Copyright John Maddock 2006.
0002 //  Copyright Matt Borland 2024
0003 //  Use, modification and distribution are subject to the
0004 //  Boost Software License, Version 1.0. (See accompanying file
0005 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0006
0007 #ifndef BOOST_STATS_EXPONENTIAL_HPP
0008 #define BOOST_STATS_EXPONENTIAL_HPP
0009
0010 #include <boost/math/tools/config.hpp>
0011 #include <boost/math/tools/tuple.hpp>
0012 #include <boost/math/tools/numeric_limits.hpp>
0013 #include <boost/math/constants/constants.hpp>
0014 #include <boost/math/special_functions/log1p.hpp>
0015 #include <boost/math/special_functions/expm1.hpp>
0016 #include <boost/math/distributions/complement.hpp>
0017 #include <boost/math/distributions/detail/common_error_handling.hpp>
0018 #include <boost/math/policies/policy.hpp>
0019 #include <boost/math/policies/error_handling.hpp>
0020
0021 #ifdef _MSC_VER
0022 # pragma warning(push)
0023 # pragma warning(disable: 4127) // conditional expression is constant
0024 # pragma warning(disable: 4702) // unreachable code (return after domain_error throw).
0025 #endif
0026
0027 #ifndef BOOST_MATH_HAS_NVRTC
0028 #include <boost/math/distributions/fwd.hpp>
0029 #include <utility>
0030 #include <cmath>
0031 #endif
0032
0033 namespace boost{ namespace math{
0034
0035 namespace detail{
0036 //
0037 // Error check:
0038 //
0039 template <class RealType, class Policy>
0040 BOOST_MATH_GPU_ENABLED inline bool verify_lambda(const char* function, RealType l, RealType* presult, const Policy& pol)
0041 {
0042    if((l <= 0) || !(boost::math::isfinite)(l))
0043    {
0044       *presult = policies::raise_domain_error<RealType>(
0045          function,
0046          "The scale parameter \"lambda\" must be > 0, but was: %1%.", l, pol);
0047       return false;
0048    }
0049    return true;
0050 }
0051
0052 template <class RealType, class Policy>
0053 BOOST_MATH_GPU_ENABLED inline bool verify_exp_x(const char* function, RealType x, RealType* presult, const Policy& pol)
0054 {
0055    if((x < 0) || (boost::math::isnan)(x))
0056    {
0057       *presult = policies::raise_domain_error<RealType>(
0058          function,
0059          "The random variable must be >= 0, but was: %1%.", x, pol);
0060       return false;
0061    }
0062    return true;
0063 }
0064
0065 } // namespace detail
0066
0067 template <class RealType = double, class Policy = policies::policy<> >
0068 class exponential_distribution
0069 {
0070 public:
0071    using value_type = RealType;
0072    using policy_type = Policy;
0073
0074    BOOST_MATH_GPU_ENABLED explicit exponential_distribution(RealType l_lambda = 1)
0075       : m_lambda(l_lambda)
0076    {
0077       RealType err;
0078       detail::verify_lambda("boost::math::exponential_distribution<%1%>::exponential_distribution", l_lambda, &err, Policy());
0079    } // exponential_distribution
0080
0081    BOOST_MATH_GPU_ENABLED RealType lambda()const { return m_lambda; }
0082
0083 private:
0084    RealType m_lambda;
0085 };
0086
0087 using exponential = exponential_distribution<double>;
0088
0089 #ifdef __cpp_deduction_guides
0090 template <class RealType>
0091 exponential_distribution(RealType)->exponential_distribution<typename boost::math::tools::promote_args<RealType>::type>;
0092 #endif
0093
0094 template <class RealType, class Policy>
0095 BOOST_MATH_GPU_ENABLED inline boost::math::pair<RealType, RealType> range(const exponential_distribution<RealType, Policy>& /*dist*/)
0096 { // Range of permissible values for random variable x.
0097   BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<RealType>::has_infinity)
0098   {
0099     return boost::math::pair<RealType, RealType>(static_cast<RealType>(0), boost::math::numeric_limits<RealType>::infinity()); // 0 to + infinity.
0100   }
0101   else
0102   {
0103    using boost::math::tools::max_value;
0104    return boost::math::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max
0105   }
0106 }
0107
0108 template <class RealType, class Policy>
0109 BOOST_MATH_GPU_ENABLED inline boost::math::pair<RealType, RealType> support(const exponential_distribution<RealType, Policy>& /*dist*/)
0110 { // Range of supported values for random variable x.
0111    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
0112    using boost::math::tools::max_value;
0113    using boost::math::tools::min_value;
0114    return boost::math::pair<RealType, RealType>(min_value<RealType>(),  max_value<RealType>());
0115    // min_value<RealType>() to avoid a discontinuity at x = 0.
0116 }
0117
0118 template <class RealType, class Policy>
0119 BOOST_MATH_GPU_ENABLED inline RealType pdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
0120 {
0121    BOOST_MATH_STD_USING // for ADL of std functions
0122
0123    constexpr auto function = "boost::math::pdf(const exponential_distribution<%1%>&, %1%)";
0124
0125    RealType lambda = dist.lambda();
0126    RealType result = 0;
0127    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0128       return result;
0129    if(0 == detail::verify_exp_x(function, x, &result, Policy()))
0130       return result;
0131    // Workaround for VC11/12 bug:
0132    if ((boost::math::isinf)(x))
0133       return 0;
0134    result = lambda * exp(-lambda * x);
0135    return result;
0136 } // pdf
0137
0138 template <class RealType, class Policy>
0139 BOOST_MATH_GPU_ENABLED inline RealType logpdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
0140 {
0141    BOOST_MATH_STD_USING // for ADL of std functions
0142
0143    constexpr auto function = "boost::math::logpdf(const exponential_distribution<%1%>&, %1%)";
0144
0145    RealType lambda = dist.lambda();
0146    RealType result = -boost::math::numeric_limits<RealType>::infinity();
0147    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0148       return result;
0149    if(0 == detail::verify_exp_x(function, x, &result, Policy()))
0150       return result;
0151
0152    result = log(lambda) - lambda * x;
0153    return result;
0154 } // logpdf
0155
0156 template <class RealType, class Policy>
0157 BOOST_MATH_GPU_ENABLED inline RealType cdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
0158 {
0159    BOOST_MATH_STD_USING // for ADL of std functions
0160
0161    constexpr auto function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)";
0162
0163    RealType result = 0;
0164    RealType lambda = dist.lambda();
0165    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0166       return result;
0167    if(0 == detail::verify_exp_x(function, x, &result, Policy()))
0168       return result;
0169    result = -boost::math::expm1(-x * lambda, Policy());
0170
0171    return result;
0172 } // cdf
0173
0174 template <class RealType, class Policy>
0175 BOOST_MATH_GPU_ENABLED inline RealType logcdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
0176 {
0177    BOOST_MATH_STD_USING // for ADL of std functions
0178
0179    constexpr auto function = "boost::math::logcdf(const exponential_distribution<%1%>&, %1%)";
0180
0181    RealType result = 0;
0182    RealType lambda = dist.lambda();
0183    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0184       return result;
0185    if(0 == detail::verify_exp_x(function, x, &result, Policy()))
0186       return result;
0187    result = boost::math::log1p(-exp(-x * lambda), Policy());
0188
0189    return result;
0190 } // cdf
0191
0192 template <class RealType, class Policy>
0193 BOOST_MATH_GPU_ENABLED inline RealType quantile(const exponential_distribution<RealType, Policy>& dist, const RealType& p)
0194 {
0195    BOOST_MATH_STD_USING // for ADL of std functions
0196
0197    constexpr auto function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)";
0198
0199    RealType result = 0;
0200    RealType lambda = dist.lambda();
0201    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0202       return result;
0203    if(0 == detail::check_probability(function, p, &result, Policy()))
0204       return result;
0205
0206    if(p == 0)
0207       return 0;
0208    if(p == 1)
0209       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0210
0211    result = -boost::math::log1p(-p, Policy()) / lambda;
0212    return result;
0213 } // quantile
0214
0215 template <class RealType, class Policy>
0216 BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
0217 {
0218    BOOST_MATH_STD_USING // for ADL of std functions
0219
0220    constexpr auto function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)";
0221
0222    RealType result = 0;
0223    RealType lambda = c.dist.lambda();
0224    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0225       return result;
0226    if(0 == detail::verify_exp_x(function, c.param, &result, Policy()))
0227       return result;
0228    // Workaround for VC11/12 bug:
0229    if (c.param >= tools::max_value<RealType>())
0230       return 0;
0231    result = exp(-c.param * lambda);
0232
0233    return result;
0234 }
0235
0236 template <class RealType, class Policy>
0237 BOOST_MATH_GPU_ENABLED inline RealType logcdf(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
0238 {
0239    BOOST_MATH_STD_USING // for ADL of std functions
0240
0241    constexpr auto function = "boost::math::logcdf(const exponential_distribution<%1%>&, %1%)";
0242
0243    RealType result = 0;
0244    RealType lambda = c.dist.lambda();
0245    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0246       return result;
0247    if(0 == detail::verify_exp_x(function, c.param, &result, Policy()))
0248       return result;
0249    // Workaround for VC11/12 bug:
0250    if (c.param >= tools::max_value<RealType>())
0251       return 0;
0252    result = -c.param * lambda;
0253
0254    return result;
0255 }
0256
0257 template <class RealType, class Policy>
0258 BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
0259 {
0260    BOOST_MATH_STD_USING // for ADL of std functions
0261
0262    constexpr auto function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)";
0263
0264    RealType result = 0;
0265    RealType lambda = c.dist.lambda();
0266    if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
0267       return result;
0268
0269    RealType q = c.param;
0270    if(0 == detail::check_probability(function, q, &result, Policy()))
0271       return result;
0272
0273    if(q == 1)
0274       return 0;
0275    if(q == 0)
0276       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0277
0278    result = -log(q) / lambda;
0279    return result;
0280 }
0281
0282 template <class RealType, class Policy>
0283 BOOST_MATH_GPU_ENABLED inline RealType mean(const exponential_distribution<RealType, Policy>& dist)
0284 {
0285    RealType result = 0;
0286    RealType lambda = dist.lambda();
0287    if(0 == detail::verify_lambda("boost::math::mean(const exponential_distribution<%1%>&)", lambda, &result, Policy()))
0288       return result;
0289    return 1 / lambda;
0290 }
0291
0292 template <class RealType, class Policy>
0293 BOOST_MATH_GPU_ENABLED inline RealType standard_deviation(const exponential_distribution<RealType, Policy>& dist)
0294 {
0295    RealType result = 0;
0296    RealType lambda = dist.lambda();
0297    if(0 == detail::verify_lambda("boost::math::standard_deviation(const exponential_distribution<%1%>&)", lambda, &result, Policy()))
0298       return result;
0299    return 1 / lambda;
0300 }
0301
0302 template <class RealType, class Policy>
0303 BOOST_MATH_GPU_ENABLED inline RealType mode(const exponential_distribution<RealType, Policy>& /*dist*/)
0304 {
0305    return 0;
0306 }
0307
0308 template <class RealType, class Policy>
0309 BOOST_MATH_GPU_ENABLED inline RealType median(const exponential_distribution<RealType, Policy>& dist)
0310 {
0311    using boost::math::constants::ln_two;
0312    return ln_two<RealType>() / dist.lambda(); // ln(2) / lambda
0313 }
0314
0315 template <class RealType, class Policy>
0316 BOOST_MATH_GPU_ENABLED inline RealType skewness(const exponential_distribution<RealType, Policy>& /*dist*/)
0317 {
0318    return 2;
0319 }
0320
0321 template <class RealType, class Policy>
0322 BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const exponential_distribution<RealType, Policy>& /*dist*/)
0323 {
0324    return 9;
0325 }
0326
0327 template <class RealType, class Policy>
0328 BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const exponential_distribution<RealType, Policy>& /*dist*/)
0329 {
0330    return 6;
0331 }
0332
0333 template <class RealType, class Policy>
0334 BOOST_MATH_GPU_ENABLED inline RealType entropy(const exponential_distribution<RealType, Policy>& dist)
0335 {
0336    using std::log;
0337    return 1 - log(dist.lambda());
0338 }
0339
0340 } // namespace math
0341 } // namespace boost
0342
0343 #ifdef _MSC_VER
0344 # pragma warning(pop)
0345 #endif
0346
0347 // This include must be at the end, *after* the accessors
0348 // for this distribution have been defined, in order to
0349 // keep compilers that support two-phase lookup happy.
0350 #include <boost/math/distributions/detail/derived_accessors.hpp>
0351
0352 #endif // BOOST_STATS_EXPONENTIAL_HPP