comparison DEPENDENCIES/generic/include/boost/math/distributions/hyperexponential.hpp @ 102:f46d142149f5

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+//  Copyright 2014 Marco Guazzone ([e-mail])
+//
+//  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)
+//
+// This module implements the Hyper-Exponential distribution.
+//
+// References:
+// - "Queueing Theory in Manufacturing Systems Analysis and Design" by H.T. Papadopolous, C. Heavey and J. Browne (Chapman & Hall/CRC, 1993)
+// - http://reference.wolfram.com/language/ref/HyperexponentialDistribution.html
+// - http://en.wikipedia.org/wiki/Hyperexponential_distribution
+//
+
+#ifndef BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL_HPP
+#define BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL_HPP
+
+
+#include <boost/config.hpp>
+#include <boost/math/distributions/complement.hpp>
+#include <boost/math/distributions/detail/common_error_handling.hpp>
+#include <boost/math/distributions/exponential.hpp>
+#include <boost/math/policies/policy.hpp>
+#include <boost/math/special_functions/fpclassify.hpp>
+#include <boost/math/tools/precision.hpp>
+#include <boost/math/tools/roots.hpp>
+#include <boost/range/begin.hpp>
+#include <boost/range/end.hpp>
+#include <boost/range/size.hpp>
+#include <boost/type_traits/has_pre_increment.hpp>
+#include <cstddef>
+#include <iterator>
+#include <limits>
+#include <numeric>
+#include <utility>
+#include <vector>
+
+#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST)
+# include <initializer_list>
+#endif
+
+#ifdef _MSC_VER
+# pragma warning (push)
+# pragma warning(disable:4127) // conditional expression is constant
+# pragma warning(disable:4389) // '==' : signed/unsigned mismatch in test_tools
+#endif // _MSC_VER
+
+namespace boost { namespace math {
+
+namespace detail {
+
+template <typename Dist>
+typename Dist::value_type generic_quantile(const Dist& dist, const typename Dist::value_type& p, const typename Dist::value_type& guess, bool comp, const char* function);
+
+} // Namespace detail
+
+
+template <typename RealT, typename PolicyT>
+class hyperexponential_distribution;
+
+
+namespace /*<unnamed>*/ { namespace hyperexp_detail {
+
+template <typename T>
+void normalize(std::vector<T>& v)
+{
+   if(!v.size())
+      return;  // Our error handlers will get this later
+    const T sum = std::accumulate(v.begin(), v.end(), static_cast<T>(0));
+    T final_sum = 0;
+    const typename std::vector<T>::iterator end = --v.end();
+    for (typename std::vector<T>::iterator it = v.begin();
+         it != end;
+         ++it)
+    {
+        *it /= sum;
+        final_sum += *it;
+    }
+    *end = 1 - final_sum;  // avoids round off errors, ensures the probs really do sum to 1.
+}
+
+template <typename RealT, typename PolicyT>
+bool check_probabilities(char const* function, std::vector<RealT> const& probabilities, RealT* presult, PolicyT const& pol)
+{
+    BOOST_MATH_STD_USING
+    const std::size_t n = probabilities.size();
+    RealT sum = 0;
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        if (probabilities[i] < 0
+            || probabilities[i] > 1
+            || !(boost::math::isfinite)(probabilities[i]))
+        {
+            *presult = policies::raise_domain_error<RealT>(function,
+                                                           "The elements of parameter \"probabilities\" must be >= 0 and <= 1, but at least one of them was: %1%.",
+                                                           probabilities[i],
+                                                           pol);
+            return false;
+        }
+        sum += probabilities[i];
+    }
+
+    //
+    // We try to keep phase probabilities correctly normalized in the distribution constructors,
+    // however in practice we have to allow for a very slight divergence from a sum of exactly 1:
+    //
+    if (fabs(sum - 1) > tools::epsilon<RealT>() * 2)
+    {
+        *presult = policies::raise_domain_error<RealT>(function,
+                                                       "The elements of parameter \"probabilities\" must sum to 1, but their sum is: %1%.",
+                                                       sum,
+                                                       pol);
+        return false;
+    }
+
+    return true;
+}
+
+template <typename RealT, typename PolicyT>
+bool check_rates(char const* function, std::vector<RealT> const& rates, RealT* presult, PolicyT const& pol)
+{
+    const std::size_t n = rates.size();
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        if (rates[i] <= 0
+            || !(boost::math::isfinite)(rates[i]))
+        {
+            *presult = policies::raise_domain_error<RealT>(function,
+                                                           "The elements of parameter \"rates\" must be > 0, but at least one of them is: %1%.",
+                                                           rates[i],
+                                                           pol);
+            return false;
+        }
+    }
+    return true;
+}
+
+template <typename RealT, typename PolicyT>
+bool check_dist(char const* function, std::vector<RealT> const& probabilities, std::vector<RealT> const& rates, RealT* presult, PolicyT const& pol)
+{
+    BOOST_MATH_STD_USING
+    if (probabilities.size() != rates.size())
+    {
+        *presult = policies::raise_domain_error<RealT>(function,
+                                                       "The parameters \"probabilities\" and \"rates\" must have the same length, but their size differ by: %1%.",
+                                                       fabs(static_cast<RealT>(probabilities.size())-static_cast<RealT>(rates.size())),
+                                                       pol);
+        return false;
+    }
+
+    return check_probabilities(function, probabilities, presult, pol)
+           && check_rates(function, rates, presult, pol);
+}
+
+template <typename RealT, typename PolicyT>
+bool check_x(char const* function, RealT x, RealT* presult, PolicyT const& pol)
+{
+    if (x < 0 || (boost::math::isnan)(x))
+    {
+        *presult = policies::raise_domain_error<RealT>(function, "The random variable must be >= 0, but is: %1%.", x, pol);
+        return false;
+    }
+    return true;
+}
+
+template <typename RealT, typename PolicyT>
+bool check_probability(char const* function, RealT p, RealT* presult, PolicyT const& pol)
+{
+    if (p < 0 || p > 1 || (boost::math::isnan)(p))
+    {
+        *presult = policies::raise_domain_error<RealT>(function, "The probability be >= 0 and <= 1, but is: %1%.", p, pol);
+        return false;
+    }
+    return true;
+}
+
+template <typename RealT, typename PolicyT>
+RealT quantile_impl(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& p, bool comp)
+{
+    // Don't have a closed form so try to numerically solve the inverse CDF...
+
+    typedef typename policies::evaluation<RealT, PolicyT>::type value_type;
+    typedef typename policies::normalise<PolicyT,
+                                         policies::promote_float<false>,
+                                         policies::promote_double<false>,
+                                         policies::discrete_quantile<>,
+                                         policies::assert_undefined<> >::type forwarding_policy;
+
+    static const char* function = comp ? "boost::math::quantile(const boost::math::complemented2_type<boost::math::hyperexponential_distribution<%1%>, %1%>&)"
+                                       : "boost::math::quantile(const boost::math::hyperexponential_distribution<%1%>&, %1%)";
+
+    RealT result = 0;
+
+    if (!check_probability(function, p, &result, PolicyT()))
+    {
+        return result;
+    }
+
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    // A possible (but inaccurate) approximation is given below, where the
+    // quantile is given by the weighted sum of exponential quantiles:
+    RealT guess = 0;
+    if (comp)
+    {
+        for (std::size_t i = 0; i < n; ++i)
+        {
+            const exponential_distribution<RealT,PolicyT> exp(rates[i]);
+
+            guess += probs[i]*quantile(complement(exp, p));
+        }
+    }
+    else
+    {
+        for (std::size_t i = 0; i < n; ++i)
+        {
+            const exponential_distribution<RealT,PolicyT> exp(rates[i]);
+
+            guess += probs[i]*quantile(exp, p);
+        }
+    }
+
+    // Fast return in case the Hyper-Exponential is essentially an Exponential
+    if (n == 1)
+    {
+        return guess;
+    }
+
+    value_type q;
+    q = detail::generic_quantile(hyperexponential_distribution<RealT,forwarding_policy>(probs, rates),
+                                 p,
+                                 guess,
+                                 comp,
+                                 function);
+
+    result = policies::checked_narrowing_cast<RealT,forwarding_policy>(q, function);
+
+    return result;
+}
+
+}} // Namespace <unnamed>::hyperexp_detail
+
+
+template <typename RealT = double, typename PolicyT = policies::policy<> >
+class hyperexponential_distribution
+{
+    public: typedef RealT value_type;
+    public: typedef PolicyT policy_type;
+
+
+    public: hyperexponential_distribution()
+    : probs_(1, 1),
+      rates_(1, 1)
+    {
+        RealT err;
+        hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution",
+                                    probs_,
+                                    rates_,
+                                    &err,
+                                    PolicyT());
+    }
+
+    // Four arg constructor: no ambiguity here, the arguments must be two pairs of iterators:
+    public: template <typename ProbIterT, typename RateIterT>
+            hyperexponential_distribution(ProbIterT prob_first, ProbIterT prob_last,
+                                          RateIterT rate_first, RateIterT rate_last)
+    : probs_(prob_first, prob_last),
+      rates_(rate_first, rate_last)
+    {
+        hyperexp_detail::normalize(probs_);
+        RealT err;
+        hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution",
+                                    probs_,
+                                    rates_,
+                                    &err,
+                                    PolicyT());
+    }
+
+    // Two arg constructor from 2 ranges, we SFINAE this out of existance if
+    // either argument type is incrementable as in that case the type is
+    // probably an iterator:
+    public: template <typename ProbRangeT, typename RateRangeT>
+            hyperexponential_distribution(ProbRangeT const& prob_range,
+                                          RateRangeT const& rate_range,
+                                          typename boost::disable_if_c<boost::has_pre_increment<ProbRangeT>::value || boost::has_pre_increment<RateRangeT>::value>::type* = 0)
+    : probs_(boost::begin(prob_range), boost::end(prob_range)),
+      rates_(boost::begin(rate_range), boost::end(rate_range))
+    {
+        hyperexp_detail::normalize(probs_);
+
+        RealT err;
+        hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution",
+                                    probs_,
+                                    rates_,
+                                    &err,
+                                    PolicyT());
+    }
+
+    // Two arg constructor for a pair of iterators: we SFINAE this out of
+    // existance if neither argument types are incrementable.
+    // Note that we allow different argument types here to allow for
+    // construction from an array plus a pointer into that array.
+    public: template <typename RateIterT, typename RateIterT2>
+            hyperexponential_distribution(RateIterT const& rate_first, 
+                                          RateIterT2 const& rate_last, 
+                                          typename boost::enable_if_c<boost::has_pre_increment<RateIterT>::value || boost::has_pre_increment<RateIterT2>::value>::type* = 0)
+    : probs_(std::distance(rate_first, rate_last), 1), // will be normalized below
+      rates_(rate_first, rate_last)
+    {
+        hyperexp_detail::normalize(probs_);
+
+        RealT err;
+        hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution",
+                                    probs_,
+                                    rates_,
+                                    &err,
+                                    PolicyT());
+    }
+
+#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST)
+      // Initializer list constructor: allows for construction from array literals:
+public: hyperexponential_distribution(std::initializer_list<RealT> l1, std::initializer_list<RealT> l2)
+      : probs_(l1.begin(), l1.end()),
+        rates_(l2.begin(), l2.end())
+      {
+         hyperexp_detail::normalize(probs_);
+
+         RealT err;
+         hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution",
+            probs_,
+            rates_,
+            &err,
+            PolicyT());
+      }
+
+public: hyperexponential_distribution(std::initializer_list<RealT> l1)
+      : probs_(l1.size(), 1),
+        rates_(l1.begin(), l1.end())
+      {
+         hyperexp_detail::normalize(probs_);
+
+         RealT err;
+         hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution",
+            probs_,
+            rates_,
+            &err,
+            PolicyT());
+      }
+#endif // !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST)
+
+    // Single argument constructor: argument must be a range.
+    public: template <typename RateRangeT>
+    hyperexponential_distribution(RateRangeT const& rate_range)
+    : probs_(boost::size(rate_range), 1), // will be normalized below
+      rates_(boost::begin(rate_range), boost::end(rate_range))
+    {
+        hyperexp_detail::normalize(probs_);
+
+        RealT err;
+        hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution",
+                                    probs_,
+                                    rates_,
+                                    &err,
+                                    PolicyT());
+    }
+
+    public: std::vector<RealT> probabilities() const
+    {
+        return probs_;
+    }
+
+    public: std::vector<RealT> rates() const
+    {
+        return rates_;
+    }
+
+    public: std::size_t num_phases() const
+    {
+        return rates_.size();
+    }
+
+
+    private: std::vector<RealT> probs_;
+    private: std::vector<RealT> rates_;
+}; // class hyperexponential_distribution
+
+
+// Convenient type synonym for double.
+typedef hyperexponential_distribution<double> hyperexponential;
+
+
+// Range of permissible values for random variable x
+template <typename RealT, typename PolicyT>
+std::pair<RealT,RealT> range(hyperexponential_distribution<RealT,PolicyT> const&)
+{
+    if (std::numeric_limits<RealT>::has_infinity)
+    {
+        return std::make_pair(static_cast<RealT>(0), std::numeric_limits<RealT>::infinity()); // 0 to +inf.
+    }
+
+    return std::make_pair(static_cast<RealT>(0), tools::max_value<RealT>()); // 0 to +<max value>
+}
+
+// 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.
+template <typename RealT, typename PolicyT>
+std::pair<RealT,RealT> support(hyperexponential_distribution<RealT,PolicyT> const&)
+{
+    return std::make_pair(tools::min_value<RealT>(), tools::max_value<RealT>()); // <min value> to +<max value>.
+}
+
+template <typename RealT, typename PolicyT>
+RealT pdf(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& x)
+{
+    BOOST_MATH_STD_USING
+    RealT result = 0;
+
+    if (!hyperexp_detail::check_x("boost::math::pdf(const boost::math::hyperexponential_distribution<%1%>&, %1%)", x, &result, PolicyT()))
+    {
+        return result;
+    }
+
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        const exponential_distribution<RealT,PolicyT> exp(rates[i]);
+
+        result += probs[i]*pdf(exp, x);
+        //result += probs[i]*rates[i]*exp(-rates[i]*x);
+    }
+
+    return result;
+}
+
+template <typename RealT, typename PolicyT>
+RealT cdf(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& x)
+{
+    RealT result = 0;
+
+    if (!hyperexp_detail::check_x("boost::math::cdf(const boost::math::hyperexponential_distribution<%1%>&, %1%)", x, &result, PolicyT()))
+    {
+        return result;
+    }
+
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        const exponential_distribution<RealT,PolicyT> exp(rates[i]);
+
+        result += probs[i]*cdf(exp, x);
+    }
+
+    return result;
+}
+
+template <typename RealT, typename PolicyT>
+RealT quantile(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& p)
+{
+    return hyperexp_detail::quantile_impl(dist, p , false);
+}
+
+template <typename RealT, typename PolicyT>
+RealT cdf(complemented2_type<hyperexponential_distribution<RealT,PolicyT>, RealT> const& c)
+{
+    RealT const& x = c.param;
+    hyperexponential_distribution<RealT,PolicyT> const& dist = c.dist;
+
+    RealT result = 0;
+
+    if (!hyperexp_detail::check_x("boost::math::cdf(boost::math::complemented2_type<const boost::math::hyperexponential_distribution<%1%>&, %1%>)", x, &result, PolicyT()))
+    {
+        return result;
+    }
+
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        const exponential_distribution<RealT,PolicyT> exp(rates[i]);
+
+        result += probs[i]*cdf(complement(exp, x));
+    }
+
+    return result;
+}
+
+
+template <typename RealT, typename PolicyT>
+RealT quantile(complemented2_type<hyperexponential_distribution<RealT, PolicyT>, RealT> const& c)
+{
+    RealT const& p = c.param;
+    hyperexponential_distribution<RealT,PolicyT> const& dist = c.dist;
+
+    return hyperexp_detail::quantile_impl(dist, p , true);
+}
+
+template <typename RealT, typename PolicyT>
+RealT mean(hyperexponential_distribution<RealT, PolicyT> const& dist)
+{
+    RealT result = 0;
+
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        const exponential_distribution<RealT,PolicyT> exp(rates[i]);
+
+        result += probs[i]*mean(exp);
+    }
+
+    return result;
+}
+
+template <typename RealT, typename PolicyT>
+RealT variance(hyperexponential_distribution<RealT, PolicyT> const& dist)
+{
+    RealT result = 0;
+
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        result += probs[i]/(rates[i]*rates[i]);
+    }
+
+    const RealT mean = boost::math::mean(dist);
+
+    result = 2*result-mean*mean;
+
+    return result;
+}
+
+template <typename RealT, typename PolicyT>
+RealT skewness(hyperexponential_distribution<RealT,PolicyT> const& dist)
+{
+    BOOST_MATH_STD_USING
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    RealT s1 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i}
+    RealT s2 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^2}
+    RealT s3 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^3}
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        const RealT p = probs[i];
+        const RealT r = rates[i];
+        const RealT r2 = r*r;
+        const RealT r3 = r2*r;
+
+        s1 += p/r;
+        s2 += p/r2;
+        s3 += p/r3;
+    }
+
+    const RealT s1s1 = s1*s1;
+
+    const RealT num = (6*s3 - (3*(2*s2 - s1s1) + s1s1)*s1);
+    const RealT den = (2*s2 - s1s1);
+
+    return num / pow(den, static_cast<RealT>(1.5));
+}
+
+template <typename RealT, typename PolicyT>
+RealT kurtosis(hyperexponential_distribution<RealT,PolicyT> const& dist)
+{
+    const std::size_t n = dist.num_phases();
+    const std::vector<RealT> probs = dist.probabilities();
+    const std::vector<RealT> rates = dist.rates();
+
+    RealT s1 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i}
+    RealT s2 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^2}
+    RealT s3 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^3}
+    RealT s4 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^4}
+    for (std::size_t i = 0; i < n; ++i)
+    {
+        const RealT p = probs[i];
+        const RealT r = rates[i];
+        const RealT r2 = r*r;
+        const RealT r3 = r2*r;
+        const RealT r4 = r3*r;
+
+        s1 += p/r;
+        s2 += p/r2;
+        s3 += p/r3;
+        s4 += p/r4;
+    }
+
+    const RealT s1s1 = s1*s1;
+
+    const RealT num = (24*s4 - 24*s3*s1 + 3*(2*(2*s2 - s1s1) + s1s1)*s1s1);
+    const RealT den = (2*s2 - s1s1);
+
+    return num/(den*den);
+}
+
+template <typename RealT, typename PolicyT>
+RealT kurtosis_excess(hyperexponential_distribution<RealT,PolicyT> const& dist)
+{
+    return kurtosis(dist) - 3;
+}
+
+template <typename RealT, typename PolicyT>
+RealT mode(hyperexponential_distribution<RealT,PolicyT> const& /*dist*/)
+{
+    return 0;
+}
+
+}} // namespace boost::math
+
+#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>
+#include <boost/math/distributions/detail/generic_quantile.hpp>
+
+#endif // BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL