math/distributions/weibull.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_WEIBULL_HPP
0008 #define BOOST_STATS_WEIBULL_HPP
0009
0010 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
0011 // http://mathworld.wolfram.com/WeibullDistribution.html
0012
0013 #include <boost/math/tools/config.hpp>
0014 #include <boost/math/tools/numeric_limits.hpp>
0015 #include <boost/math/tools/type_traits.hpp>
0016 #include <boost/math/tools/cstdint.hpp>
0017 #include <boost/math/distributions/fwd.hpp>
0018 #include <boost/math/special_functions/gamma.hpp>
0019 #include <boost/math/special_functions/log1p.hpp>
0020 #include <boost/math/special_functions/expm1.hpp>
0021 #include <boost/math/distributions/detail/common_error_handling.hpp>
0022 #include <boost/math/distributions/complement.hpp>
0023
0024 namespace boost{ namespace math
0025 {
0026 namespace detail{
0027
0028 template <class RealType, class Policy>
0029 BOOST_MATH_GPU_ENABLED inline bool check_weibull_shape(
0030       const char* function,
0031       RealType shape,
0032       RealType* result, const Policy& pol)
0033 {
0034    if((shape <= 0) || !(boost::math::isfinite)(shape))
0035    {
0036       *result = policies::raise_domain_error<RealType>(
0037          function,
0038          "Shape parameter is %1%, but must be > 0 !", shape, pol);
0039       return false;
0040    }
0041    return true;
0042 }
0043
0044 template <class RealType, class Policy>
0045 BOOST_MATH_GPU_ENABLED inline bool check_weibull_x(
0046       const char* function,
0047       RealType const& x,
0048       RealType* result, const Policy& pol)
0049 {
0050    if((x < 0) || !(boost::math::isfinite)(x))
0051    {
0052       *result = policies::raise_domain_error<RealType>(
0053          function,
0054          "Random variate is %1% but must be >= 0 !", x, pol);
0055       return false;
0056    }
0057    return true;
0058 }
0059
0060 template <class RealType, class Policy>
0061 BOOST_MATH_GPU_ENABLED inline bool check_weibull(
0062       const char* function,
0063       RealType scale,
0064       RealType shape,
0065       RealType* result, const Policy& pol)
0066 {
0067    return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol);
0068 }
0069
0070 } // namespace detail
0071
0072 template <class RealType = double, class Policy = policies::policy<> >
0073 class weibull_distribution
0074 {
0075 public:
0076    using value_type = RealType;
0077    using policy_type = Policy;
0078
0079    BOOST_MATH_GPU_ENABLED explicit weibull_distribution(RealType l_shape, RealType l_scale = 1)
0080       : m_shape(l_shape), m_scale(l_scale)
0081    {
0082       RealType result;
0083       detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy());
0084    }
0085
0086    BOOST_MATH_GPU_ENABLED RealType shape()const
0087    {
0088       return m_shape;
0089    }
0090
0091    BOOST_MATH_GPU_ENABLED RealType scale()const
0092    {
0093       return m_scale;
0094    }
0095 private:
0096    //
0097    // Data members:
0098    //
0099    RealType m_shape;     // distribution shape
0100    RealType m_scale;     // distribution scale
0101 };
0102
0103 using weibull = weibull_distribution<double>;
0104
0105 #ifdef __cpp_deduction_guides
0106 template <class RealType>
0107 weibull_distribution(RealType)->weibull_distribution<typename boost::math::tools::promote_args<RealType>::type>;
0108 template <class RealType>
0109 weibull_distribution(RealType,RealType)->weibull_distribution<typename boost::math::tools::promote_args<RealType>::type>;
0110 #endif
0111
0112 template <class RealType, class Policy>
0113 BOOST_MATH_GPU_ENABLED inline boost::math::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/)
0114 { // Range of permissible values for random variable x.
0115    using boost::math::tools::max_value;
0116    return boost::math::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
0117 }
0118
0119 template <class RealType, class Policy>
0120 BOOST_MATH_GPU_ENABLED inline boost::math::pair<RealType, RealType> support(const weibull_distribution<RealType, Policy>& /*dist*/)
0121 { // Range of supported values for random variable x.
0122    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
0123    using boost::math::tools::max_value;
0124    using boost::math::tools::min_value;
0125    return boost::math::pair<RealType, RealType>(min_value<RealType>(),  max_value<RealType>());
0126    // A discontinuity at x == 0, so only support down to min_value.
0127 }
0128
0129 template <class RealType, class Policy>
0130 BOOST_MATH_GPU_ENABLED inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0131 {
0132    BOOST_MATH_STD_USING  // for ADL of std functions
0133
0134    constexpr auto function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";
0135
0136    RealType shape = dist.shape();
0137    RealType scale = dist.scale();
0138
0139    RealType result = 0;
0140    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0141       return result;
0142    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0143       return result;
0144
0145    if(x == 0)
0146    {
0147       if(shape == 1)
0148       {
0149          return 1 / scale;
0150       }
0151       if(shape > 1)
0152       {
0153          return 0;
0154       }
0155       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0156    }
0157    result = exp(-pow(x / scale, shape));
0158    result *= pow(x / scale, shape - 1) * shape / scale;
0159
0160    return result;
0161 }
0162
0163 template <class RealType, class Policy>
0164 BOOST_MATH_GPU_ENABLED inline RealType logpdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0165 {
0166    BOOST_MATH_STD_USING  // for ADL of std functions
0167
0168    constexpr auto function = "boost::math::logpdf(const weibull_distribution<%1%>, %1%)";
0169
0170    RealType shape = dist.shape();
0171    RealType scale = dist.scale();
0172
0173    RealType result = 0;
0174    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0175       return result;
0176    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0177       return result;
0178
0179    if(x == 0)
0180    {
0181       if(shape == 1)
0182       {
0183          return log(1 / scale);
0184       }
0185       if(shape > 1)
0186       {
0187          return 0;
0188       }
0189       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0190    }
0191
0192    result = log(shape) - shape * log(scale) + log(x) * (shape - 1) - pow(x / scale, shape);
0193
0194    return result;
0195 }
0196
0197 template <class RealType, class Policy>
0198 BOOST_MATH_GPU_ENABLED inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0199 {
0200    BOOST_MATH_STD_USING  // for ADL of std functions
0201
0202    constexpr auto function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
0203
0204    RealType shape = dist.shape();
0205    RealType scale = dist.scale();
0206
0207    RealType result = 0;
0208    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0209       return result;
0210    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0211       return result;
0212
0213    result = -boost::math::expm1(-pow(x / scale, shape), Policy());
0214
0215    return result;
0216 }
0217
0218 template <class RealType, class Policy>
0219 BOOST_MATH_GPU_ENABLED inline RealType logcdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0220 {
0221    BOOST_MATH_STD_USING  // for ADL of std functions
0222
0223    constexpr auto function = "boost::math::logcdf(const weibull_distribution<%1%>, %1%)";
0224
0225    RealType shape = dist.shape();
0226    RealType scale = dist.scale();
0227
0228    RealType result = 0;
0229    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0230       return result;
0231    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0232       return result;
0233
0234    result = log1p(-exp(-pow(x / scale, shape)), Policy());
0235
0236    return result;
0237 }
0238
0239 template <class RealType, class Policy>
0240 BOOST_MATH_GPU_ENABLED inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
0241 {
0242    BOOST_MATH_STD_USING  // for ADL of std functions
0243
0244    constexpr auto function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
0245
0246    RealType shape = dist.shape();
0247    RealType scale = dist.scale();
0248
0249    RealType result = 0;
0250    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0251       return result;
0252    if(false == detail::check_probability(function, p, &result, Policy()))
0253       return result;
0254
0255    if(p == 1)
0256       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0257
0258    result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);
0259
0260    return result;
0261 }
0262
0263 template <class RealType, class Policy>
0264 BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
0265 {
0266    BOOST_MATH_STD_USING  // for ADL of std functions
0267
0268    constexpr auto function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
0269
0270    RealType shape = c.dist.shape();
0271    RealType scale = c.dist.scale();
0272
0273    RealType result = 0;
0274    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0275       return result;
0276    if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
0277       return result;
0278
0279    result = exp(-pow(c.param / scale, shape));
0280
0281    return result;
0282 }
0283
0284 template <class RealType, class Policy>
0285 BOOST_MATH_GPU_ENABLED inline RealType logcdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
0286 {
0287    BOOST_MATH_STD_USING  // for ADL of std functions
0288
0289    constexpr auto function = "boost::math::logcdf(const weibull_distribution<%1%>, %1%)";
0290
0291    RealType shape = c.dist.shape();
0292    RealType scale = c.dist.scale();
0293
0294    RealType result = 0;
0295    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0296       return result;
0297    if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
0298       return result;
0299
0300    result = -pow(c.param / scale, shape);
0301
0302    return result;
0303 }
0304
0305 template <class RealType, class Policy>
0306 BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
0307 {
0308    BOOST_MATH_STD_USING  // for ADL of std functions
0309
0310    constexpr auto function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
0311
0312    RealType shape = c.dist.shape();
0313    RealType scale = c.dist.scale();
0314    RealType q = c.param;
0315
0316    RealType result = 0;
0317    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0318       return result;
0319    if(false == detail::check_probability(function, q, &result, Policy()))
0320       return result;
0321
0322    if(q == 0)
0323       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0324
0325    result = scale * pow(-log(q), 1 / shape);
0326
0327    return result;
0328 }
0329
0330 template <class RealType, class Policy>
0331 BOOST_MATH_GPU_ENABLED inline RealType mean(const weibull_distribution<RealType, Policy>& dist)
0332 {
0333    BOOST_MATH_STD_USING  // for ADL of std functions
0334
0335    constexpr auto function = "boost::math::mean(const weibull_distribution<%1%>)";
0336
0337    RealType shape = dist.shape();
0338    RealType scale = dist.scale();
0339
0340    RealType result = 0;
0341    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0342       return result;
0343
0344    result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
0345    return result;
0346 }
0347
0348 template <class RealType, class Policy>
0349 BOOST_MATH_GPU_ENABLED inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
0350 {
0351    RealType shape = dist.shape();
0352    RealType scale = dist.scale();
0353
0354    constexpr auto function = "boost::math::variance(const weibull_distribution<%1%>)";
0355
0356    RealType result = 0;
0357    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0358    {
0359       return result;
0360    }
0361    result = boost::math::tgamma(1 + 1 / shape, Policy());
0362    result *= -result;
0363    result += boost::math::tgamma(1 + 2 / shape, Policy());
0364    result *= scale * scale;
0365    return result;
0366 }
0367
0368 template <class RealType, class Policy>
0369 BOOST_MATH_GPU_ENABLED inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
0370 {
0371    BOOST_MATH_STD_USING  // for ADL of std function pow.
0372
0373    constexpr auto function = "boost::math::mode(const weibull_distribution<%1%>)";
0374
0375    RealType shape = dist.shape();
0376    RealType scale = dist.scale();
0377
0378    RealType result = 0;
0379    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0380    {
0381       return result;
0382    }
0383    if(shape <= 1)
0384       return 0;
0385    result = scale * pow((shape - 1) / shape, 1 / shape);
0386    return result;
0387 }
0388
0389 template <class RealType, class Policy>
0390 BOOST_MATH_GPU_ENABLED inline RealType median(const weibull_distribution<RealType, Policy>& dist)
0391 {
0392    BOOST_MATH_STD_USING  // for ADL of std function pow.
0393
0394    constexpr auto function = "boost::math::median(const weibull_distribution<%1%>)";
0395
0396    RealType shape = dist.shape(); // Wikipedia k
0397    RealType scale = dist.scale(); // Wikipedia lambda
0398
0399    RealType result = 0;
0400    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0401    {
0402       return result;
0403    }
0404    using boost::math::constants::ln_two;
0405    result = scale * pow(ln_two<RealType>(), 1 / shape);
0406    return result;
0407 }
0408
0409 template <class RealType, class Policy>
0410 BOOST_MATH_GPU_ENABLED inline RealType skewness(const weibull_distribution<RealType, Policy>& dist)
0411 {
0412    BOOST_MATH_STD_USING  // for ADL of std functions
0413
0414    constexpr auto function = "boost::math::skewness(const weibull_distribution<%1%>)";
0415
0416    RealType shape = dist.shape();
0417    RealType scale = dist.scale();
0418
0419    RealType result = 0;
0420    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0421    {
0422       return result;
0423    }
0424
0425    RealType g1 = boost::math::tgamma(1 + 1 / shape, Policy());
0426    RealType g2 = boost::math::tgamma(1 + 2 / shape, Policy());
0427    RealType g3 = boost::math::tgamma(1 + 3 / shape, Policy());
0428    RealType d = pow(g2 - g1 * g1, RealType(1.5));
0429
0430    result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
0431    return result;
0432 }
0433
0434 template <class RealType, class Policy>
0435 BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist)
0436 {
0437    BOOST_MATH_STD_USING  // for ADL of std functions
0438
0439    constexpr auto function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";
0440
0441    RealType shape = dist.shape();
0442    RealType scale = dist.scale();
0443
0444    RealType result = 0;
0445    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0446       return result;
0447
0448    RealType g1 = boost::math::tgamma(1 + 1 / shape, Policy());
0449    RealType g2 = boost::math::tgamma(1 + 2 / shape, Policy());
0450    RealType g3 = boost::math::tgamma(1 + 3 / shape, Policy());
0451    RealType g4 = boost::math::tgamma(1 + 4 / shape, Policy());
0452    RealType g1_2 = g1 * g1;
0453    RealType g1_4 = g1_2 * g1_2;
0454    RealType d = g2 - g1_2;
0455    d *= d;
0456
0457    result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
0458    result /= d;
0459    return result;
0460 }
0461
0462 template <class RealType, class Policy>
0463 BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
0464 {
0465    return kurtosis_excess(dist) + 3;
0466 }
0467
0468 template <class RealType, class Policy>
0469 BOOST_MATH_GPU_ENABLED inline RealType entropy(const weibull_distribution<RealType, Policy>& dist)
0470 {
0471    BOOST_MATH_STD_USING
0472    RealType k = dist.shape();
0473    RealType lambda = dist.scale();
0474    return constants::euler<RealType>()*(1-1/k) + log(lambda/k) + 1;
0475 }
0476
0477 } // namespace math
0478 } // namespace boost
0479
0480 // This include must be at the end, *after* the accessors
0481 // for this distribution have been defined, in order to
0482 // keep compilers that support two-phase lookup happy.
0483 #include <boost/math/distributions/detail/derived_accessors.hpp>
0484
0485 #endif // BOOST_STATS_WEIBULL_HPP
0486
0487