boost/math/distributions/find_location.hpp
// Copyright John Maddock 2007. // Copyright Paul A. Bristow 2007. // 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_FIND_LOCATION_HPP #define BOOST_STATS_FIND_LOCATION_HPP #include <boost/math/distributions/fwd.hpp> // for all distribution signatures. #include <boost/math/distributions/complement.hpp> #include <boost/math/policies/policy.hpp> #include <boost/math/tools/traits.hpp> #include <boost/math/special_functions/fpclassify.hpp> #include <boost/math/policies/error_handling.hpp> // using boost::math::policies::policy; // using boost::math::complement; // will be needed by users who want complement, // but NOT placed here to avoid putting it in global scope. namespace boost { namespace math { // Function to find location of random variable z // to give probability p (given scale) // Applies to normal, lognormal, extreme value, Cauchy, (and symmetrical triangular), // enforced by static_assert below. template <class Dist, class Policy> inline typename Dist::value_type find_location( // For example, normal mean. typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. // For example, a nominal minimum acceptable z, so that p * 100 % are > z typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. typename Dist::value_type scale, // scale parameter, for example, normal standard deviation. const Policy& pol ) { static_assert(::boost::math::tools::is_distribution<Dist>::value, "The provided distribution does not meet the conceptual requirements of a distribution."); static_assert(::boost::math::tools::is_scaled_distribution<Dist>::value, "The provided distribution does not meet the conceptual requirements of a scaled distribution."); static const char* function = "boost::math::find_location<Dist, Policy>&, %1%)"; if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) { return policies::raise_domain_error<typename Dist::value_type>( function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, pol); } if(!(boost::math::isfinite)(z)) { return policies::raise_domain_error<typename Dist::value_type>( function, "z parameter was %1%, but must be finite!", z, pol); } if(!(boost::math::isfinite)(scale)) { return policies::raise_domain_error<typename Dist::value_type>( function, "scale parameter was %1%, but must be finite!", scale, pol); } //cout << "z " << z << ", p " << p << ", quantile(Dist(), p) " // << quantile(Dist(), p) << ", quan * scale " << quantile(Dist(), p) * scale << endl; return z - (quantile(Dist(), p) * scale); } // find_location template <class Dist> inline // with default policy. typename Dist::value_type find_location( // For example, normal mean. typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. // For example, a nominal minimum acceptable z, so that p * 100 % are > z typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. typename Dist::value_type scale) // scale parameter, for example, normal standard deviation. { // Forward to find_location with default policy. return (find_location<Dist>(z, p, scale, policies::policy<>())); } // find_location // So the user can start from the complement q = (1 - p) of the probability p, // for example, l = find_location<normal>(complement(z, q, sd)); template <class Dist, class Real1, class Real2, class Real3> inline typename Dist::value_type find_location( // Default policy. complemented3_type<Real1, Real2, Real3> const& c) { static const char* function = "boost::math::find_location<Dist, Policy>&, %1%)"; typename Dist::value_type p = c.param1; if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) { return policies::raise_domain_error<typename Dist::value_type>( function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, policies::policy<>()); } typename Dist::value_type z = c.dist; if(!(boost::math::isfinite)(z)) { return policies::raise_domain_error<typename Dist::value_type>( function, "z parameter was %1%, but must be finite!", z, policies::policy<>()); } typename Dist::value_type scale = c.param2; if(!(boost::math::isfinite)(scale)) { return policies::raise_domain_error<typename Dist::value_type>( function, "scale parameter was %1%, but must be finite!", scale, policies::policy<>()); } // cout << "z " << c.dist << ", quantile (Dist(), " << c.param1 << ") * scale " << c.param2 << endl; return z - quantile(Dist(), p) * scale; } // find_location complement template <class Dist, class Real1, class Real2, class Real3, class Real4> inline typename Dist::value_type find_location( // Explicit policy. complemented4_type<Real1, Real2, Real3, Real4> const& c) { static const char* function = "boost::math::find_location<Dist, Policy>&, %1%)"; typename Dist::value_type p = c.param1; if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) { return policies::raise_domain_error<typename Dist::value_type>( function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, c.param3); } typename Dist::value_type z = c.dist; if(!(boost::math::isfinite)(z)) { return policies::raise_domain_error<typename Dist::value_type>( function, "z parameter was %1%, but must be finite!", z, c.param3); } typename Dist::value_type scale = c.param2; if(!(boost::math::isfinite)(scale)) { return policies::raise_domain_error<typename Dist::value_type>( function, "scale parameter was %1%, but must be finite!", scale, c.param3); } // cout << "z " << c.dist << ", quantile (Dist(), " << c.param1 << ") * scale " << c.param2 << endl; return z - quantile(Dist(), p) * scale; } // find_location complement } // namespace boost } // namespace math #endif // BOOST_STATS_FIND_LOCATION_HPP