math/distributions/weibull.hpp

0001 //  Copyright John Maddock 2006.
0002 //  Use, modification and distribution are subject to the
0003 //  Boost Software License, Version 1.0. (See accompanying file
0004 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0005
0006 #ifndef BOOST_STATS_WEIBULL_HPP
0007 #define BOOST_STATS_WEIBULL_HPP
0008
0009 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
0010 // http://mathworld.wolfram.com/WeibullDistribution.html
0011
0012 #include <boost/math/distributions/fwd.hpp>
0013 #include <boost/math/special_functions/gamma.hpp>
0014 #include <boost/math/special_functions/log1p.hpp>
0015 #include <boost/math/special_functions/expm1.hpp>
0016 #include <boost/math/distributions/detail/common_error_handling.hpp>
0017 #include <boost/math/distributions/complement.hpp>
0018
0019 #include <utility>
0020
0021 namespace boost{ namespace math
0022 {
0023 namespace detail{
0024
0025 template <class RealType, class Policy>
0026 inline bool check_weibull_shape(
0027       const char* function,
0028       RealType shape,
0029       RealType* result, const Policy& pol)
0030 {
0031    if((shape <= 0) || !(boost::math::isfinite)(shape))
0032    {
0033       *result = policies::raise_domain_error<RealType>(
0034          function,
0035          "Shape parameter is %1%, but must be > 0 !", shape, pol);
0036       return false;
0037    }
0038    return true;
0039 }
0040
0041 template <class RealType, class Policy>
0042 inline bool check_weibull_x(
0043       const char* function,
0044       RealType const& x,
0045       RealType* result, const Policy& pol)
0046 {
0047    if((x < 0) || !(boost::math::isfinite)(x))
0048    {
0049       *result = policies::raise_domain_error<RealType>(
0050          function,
0051          "Random variate is %1% but must be >= 0 !", x, pol);
0052       return false;
0053    }
0054    return true;
0055 }
0056
0057 template <class RealType, class Policy>
0058 inline bool check_weibull(
0059       const char* function,
0060       RealType scale,
0061       RealType shape,
0062       RealType* result, const Policy& pol)
0063 {
0064    return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol);
0065 }
0066
0067 } // namespace detail
0068
0069 template <class RealType = double, class Policy = policies::policy<> >
0070 class weibull_distribution
0071 {
0072 public:
0073    using value_type = RealType;
0074    using policy_type = Policy;
0075
0076    explicit weibull_distribution(RealType l_shape, RealType l_scale = 1)
0077       : m_shape(l_shape), m_scale(l_scale)
0078    {
0079       RealType result;
0080       detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy());
0081    }
0082
0083    RealType shape()const
0084    {
0085       return m_shape;
0086    }
0087
0088    RealType scale()const
0089    {
0090       return m_scale;
0091    }
0092 private:
0093    //
0094    // Data members:
0095    //
0096    RealType m_shape;     // distribution shape
0097    RealType m_scale;     // distribution scale
0098 };
0099
0100 using weibull = weibull_distribution<double>;
0101
0102 #ifdef __cpp_deduction_guides
0103 template <class RealType>
0104 weibull_distribution(RealType)->weibull_distribution<typename boost::math::tools::promote_args<RealType>::type>;
0105 template <class RealType>
0106 weibull_distribution(RealType,RealType)->weibull_distribution<typename boost::math::tools::promote_args<RealType>::type>;
0107 #endif
0108
0109 template <class RealType, class Policy>
0110 inline std::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/)
0111 { // Range of permissible values for random variable x.
0112    using boost::math::tools::max_value;
0113    return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
0114 }
0115
0116 template <class RealType, class Policy>
0117 inline std::pair<RealType, RealType> support(const weibull_distribution<RealType, Policy>& /*dist*/)
0118 { // Range of supported values for random variable x.
0119    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
0120    using boost::math::tools::max_value;
0121    using boost::math::tools::min_value;
0122    return std::pair<RealType, RealType>(min_value<RealType>(),  max_value<RealType>());
0123    // A discontinuity at x == 0, so only support down to min_value.
0124 }
0125
0126 template <class RealType, class Policy>
0127 inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0128 {
0129    BOOST_MATH_STD_USING  // for ADL of std functions
0130
0131    static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";
0132
0133    RealType shape = dist.shape();
0134    RealType scale = dist.scale();
0135
0136    RealType result = 0;
0137    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0138       return result;
0139    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0140       return result;
0141
0142    if(x == 0)
0143    {
0144       if(shape == 1)
0145       {
0146          return 1 / scale;
0147       }
0148       if(shape > 1)
0149       {
0150          return 0;
0151       }
0152       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0153    }
0154    result = exp(-pow(x / scale, shape));
0155    result *= pow(x / scale, shape - 1) * shape / scale;
0156
0157    return result;
0158 }
0159
0160 template <class RealType, class Policy>
0161 inline RealType logpdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0162 {
0163    BOOST_MATH_STD_USING  // for ADL of std functions
0164
0165    static const char* function = "boost::math::logpdf(const weibull_distribution<%1%>, %1%)";
0166
0167    RealType shape = dist.shape();
0168    RealType scale = dist.scale();
0169
0170    RealType result = 0;
0171    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0172       return result;
0173    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0174       return result;
0175
0176    if(x == 0)
0177    {
0178       if(shape == 1)
0179       {
0180          return log(1 / scale);
0181       }
0182       if(shape > 1)
0183       {
0184          return 0;
0185       }
0186       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0187    }
0188
0189    result = log(shape) - shape * log(scale) + log(x) * (shape - 1) - pow(x / scale, shape);
0190
0191    return result;
0192 }
0193
0194 template <class RealType, class Policy>
0195 inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0196 {
0197    BOOST_MATH_STD_USING  // for ADL of std functions
0198
0199    static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
0200
0201    RealType shape = dist.shape();
0202    RealType scale = dist.scale();
0203
0204    RealType result = 0;
0205    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0206       return result;
0207    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0208       return result;
0209
0210    result = -boost::math::expm1(-pow(x / scale, shape), Policy());
0211
0212    return result;
0213 }
0214
0215 template <class RealType, class Policy>
0216 inline RealType logcdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
0217 {
0218    BOOST_MATH_STD_USING  // for ADL of std functions
0219
0220    static const char* function = "boost::math::logcdf(const weibull_distribution<%1%>, %1%)";
0221
0222    RealType shape = dist.shape();
0223    RealType scale = dist.scale();
0224
0225    RealType result = 0;
0226    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0227       return result;
0228    if(false == detail::check_weibull_x(function, x, &result, Policy()))
0229       return result;
0230
0231    result = log1p(-exp(-pow(x / scale, shape)), Policy());
0232
0233    return result;
0234 }
0235
0236 template <class RealType, class Policy>
0237 inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
0238 {
0239    BOOST_MATH_STD_USING  // for ADL of std functions
0240
0241    static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
0242
0243    RealType shape = dist.shape();
0244    RealType scale = dist.scale();
0245
0246    RealType result = 0;
0247    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0248       return result;
0249    if(false == detail::check_probability(function, p, &result, Policy()))
0250       return result;
0251
0252    if(p == 1)
0253       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0254
0255    result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);
0256
0257    return result;
0258 }
0259
0260 template <class RealType, class Policy>
0261 inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
0262 {
0263    BOOST_MATH_STD_USING  // for ADL of std functions
0264
0265    static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
0266
0267    RealType shape = c.dist.shape();
0268    RealType scale = c.dist.scale();
0269
0270    RealType result = 0;
0271    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0272       return result;
0273    if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
0274       return result;
0275
0276    result = exp(-pow(c.param / scale, shape));
0277
0278    return result;
0279 }
0280
0281 template <class RealType, class Policy>
0282 inline RealType logcdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
0283 {
0284    BOOST_MATH_STD_USING  // for ADL of std functions
0285
0286    static const char* function = "boost::math::logcdf(const weibull_distribution<%1%>, %1%)";
0287
0288    RealType shape = c.dist.shape();
0289    RealType scale = c.dist.scale();
0290
0291    RealType result = 0;
0292    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0293       return result;
0294    if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
0295       return result;
0296
0297    result = -pow(c.param / scale, shape);
0298
0299    return result;
0300 }
0301
0302 template <class RealType, class Policy>
0303 inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
0304 {
0305    BOOST_MATH_STD_USING  // for ADL of std functions
0306
0307    static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
0308
0309    RealType shape = c.dist.shape();
0310    RealType scale = c.dist.scale();
0311    RealType q = c.param;
0312
0313    RealType result = 0;
0314    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0315       return result;
0316    if(false == detail::check_probability(function, q, &result, Policy()))
0317       return result;
0318
0319    if(q == 0)
0320       return policies::raise_overflow_error<RealType>(function, 0, Policy());
0321
0322    result = scale * pow(-log(q), 1 / shape);
0323
0324    return result;
0325 }
0326
0327 template <class RealType, class Policy>
0328 inline RealType mean(const weibull_distribution<RealType, Policy>& dist)
0329 {
0330    BOOST_MATH_STD_USING  // for ADL of std functions
0331
0332    static const char* function = "boost::math::mean(const weibull_distribution<%1%>)";
0333
0334    RealType shape = dist.shape();
0335    RealType scale = dist.scale();
0336
0337    RealType result = 0;
0338    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0339       return result;
0340
0341    result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
0342    return result;
0343 }
0344
0345 template <class RealType, class Policy>
0346 inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
0347 {
0348    RealType shape = dist.shape();
0349    RealType scale = dist.scale();
0350
0351    static const char* function = "boost::math::variance(const weibull_distribution<%1%>)";
0352
0353    RealType result = 0;
0354    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0355    {
0356       return result;
0357    }
0358    result = boost::math::tgamma(1 + 1 / shape, Policy());
0359    result *= -result;
0360    result += boost::math::tgamma(1 + 2 / shape, Policy());
0361    result *= scale * scale;
0362    return result;
0363 }
0364
0365 template <class RealType, class Policy>
0366 inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
0367 {
0368    BOOST_MATH_STD_USING  // for ADL of std function pow.
0369
0370    static const char* function = "boost::math::mode(const weibull_distribution<%1%>)";
0371
0372    RealType shape = dist.shape();
0373    RealType scale = dist.scale();
0374
0375    RealType result = 0;
0376    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0377    {
0378       return result;
0379    }
0380    if(shape <= 1)
0381       return 0;
0382    result = scale * pow((shape - 1) / shape, 1 / shape);
0383    return result;
0384 }
0385
0386 template <class RealType, class Policy>
0387 inline RealType median(const weibull_distribution<RealType, Policy>& dist)
0388 {
0389    BOOST_MATH_STD_USING  // for ADL of std function pow.
0390
0391    static const char* function = "boost::math::median(const weibull_distribution<%1%>)";
0392
0393    RealType shape = dist.shape(); // Wikipedia k
0394    RealType scale = dist.scale(); // Wikipedia lambda
0395
0396    RealType result = 0;
0397    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0398    {
0399       return result;
0400    }
0401    using boost::math::constants::ln_two;
0402    result = scale * pow(ln_two<RealType>(), 1 / shape);
0403    return result;
0404 }
0405
0406 template <class RealType, class Policy>
0407 inline RealType skewness(const weibull_distribution<RealType, Policy>& dist)
0408 {
0409    BOOST_MATH_STD_USING  // for ADL of std functions
0410
0411    static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)";
0412
0413    RealType shape = dist.shape();
0414    RealType scale = dist.scale();
0415
0416    RealType result = 0;
0417    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0418    {
0419       return result;
0420    }
0421
0422    RealType g1 = boost::math::tgamma(1 + 1 / shape, Policy());
0423    RealType g2 = boost::math::tgamma(1 + 2 / shape, Policy());
0424    RealType g3 = boost::math::tgamma(1 + 3 / shape, Policy());
0425    RealType d = pow(g2 - g1 * g1, RealType(1.5));
0426
0427    result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
0428    return result;
0429 }
0430
0431 template <class RealType, class Policy>
0432 inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist)
0433 {
0434    BOOST_MATH_STD_USING  // for ADL of std functions
0435
0436    static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";
0437
0438    RealType shape = dist.shape();
0439    RealType scale = dist.scale();
0440
0441    RealType result = 0;
0442    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
0443       return result;
0444
0445    RealType g1 = boost::math::tgamma(1 + 1 / shape, Policy());
0446    RealType g2 = boost::math::tgamma(1 + 2 / shape, Policy());
0447    RealType g3 = boost::math::tgamma(1 + 3 / shape, Policy());
0448    RealType g4 = boost::math::tgamma(1 + 4 / shape, Policy());
0449    RealType g1_2 = g1 * g1;
0450    RealType g1_4 = g1_2 * g1_2;
0451    RealType d = g2 - g1_2;
0452    d *= d;
0453
0454    result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
0455    result /= d;
0456    return result;
0457 }
0458
0459 template <class RealType, class Policy>
0460 inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
0461 {
0462    return kurtosis_excess(dist) + 3;
0463 }
0464
0465 template <class RealType, class Policy>
0466 inline RealType entropy(const weibull_distribution<RealType, Policy>& dist)
0467 {
0468    using std::log;
0469    RealType k = dist.shape();
0470    RealType lambda = dist.scale();
0471    return constants::euler<RealType>()*(1-1/k) + log(lambda/k) + 1;
0472 }
0473
0474 } // namespace math
0475 } // namespace boost
0476
0477 // This include must be at the end, *after* the accessors
0478 // for this distribution have been defined, in order to
0479 // keep compilers that support two-phase lookup happy.
0480 #include <boost/math/distributions/detail/derived_accessors.hpp>
0481
0482 #endif // BOOST_STATS_WEIBULL_HPP
0483
0484