// Copyright John Maddock 2007.
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// Copyright Paul A. Bristow 2007.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_STATS_FIND_SCALE_HPP
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#define BOOST_STATS_FIND_SCALE_HPP
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#include <boost/math/distributions/fwd.hpp> // for all distribution signatures.
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#include <boost/math/distributions/complement.hpp>
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#include <boost/math/policies/policy.hpp>
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// using boost::math::policies::policy;
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#include <boost/math/tools/traits.hpp>
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#include <boost/static_assert.hpp>
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#include <boost/math/special_functions/fpclassify.hpp>
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#include <boost/math/policies/error_handling.hpp>
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// using boost::math::complement; // will be needed by users who want complement,
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// but NOT placed here to avoid putting it in global scope.
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namespace boost
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{
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namespace math
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{
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// Function to find location of random variable z
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// to give probability p (given scale)
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// Applies to normal, lognormal, extreme value, Cauchy, (and symmetrical triangular),
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// distributions that have scale.
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// BOOST_STATIC_ASSERTs, see below, are used to enforce this.
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template <class Dist, class Policy>
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inline
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typename Dist::value_type find_scale( // For example, normal mean.
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typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
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// For example, a nominal minimum acceptable weight z, so that p * 100 % are > z
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typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
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typename Dist::value_type location, // location parameter, for example, normal distribution mean.
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const Policy& pol
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)
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{
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#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
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BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value);
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BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value);
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#endif
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static const char* function = "boost::math::find_scale<Dist, Policy>(%1%, %1%, %1%, Policy)";
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if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, pol);
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}
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if(!(boost::math::isfinite)(z))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "find_scale z parameter was %1%, but must be finite!", z, pol);
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}
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if(!(boost::math::isfinite)(location))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "find_scale location parameter was %1%, but must be finite!", location, pol);
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}
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//cout << "z " << z << ", p " << p << ", quantile(Dist(), p) "
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//<< quantile(Dist(), p) << ", z - mean " << z - location
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//<<", sd " << (z - location) / quantile(Dist(), p) << endl;
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//quantile(N01, 0.001) -3.09023
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//quantile(N01, 0.01) -2.32635
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//quantile(N01, 0.05) -1.64485
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//quantile(N01, 0.333333) -0.430728
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//quantile(N01, 0.5) 0
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//quantile(N01, 0.666667) 0.430728
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//quantile(N01, 0.9) 1.28155
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//quantile(N01, 0.95) 1.64485
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//quantile(N01, 0.99) 2.32635
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//quantile(N01, 0.999) 3.09023
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typename Dist::value_type result =
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(z - location) // difference between desired x and current location.
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/ quantile(Dist(), p); // standard distribution.
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if (result <= 0)
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{ // If policy isn't to throw, return the scale <= 0.
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policies::raise_evaluation_error<typename Dist::value_type>(function,
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"Computed scale (%1%) is <= 0!" " Was the complement intended?",
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result, Policy());
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}
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return result;
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} // template <class Dist, class Policy> find_scale
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template <class Dist>
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inline // with default policy.
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typename Dist::value_type find_scale( // For example, normal mean.
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typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
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// For example, a nominal minimum acceptable z, so that p * 100 % are > z
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typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
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typename Dist::value_type location) // location parameter, for example, mean.
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{ // Forward to find_scale using the default policy.
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return (find_scale<Dist>(z, p, location, policies::policy<>()));
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} // find_scale
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template <class Dist, class Real1, class Real2, class Real3, class Policy>
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inline typename Dist::value_type find_scale(
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complemented4_type<Real1, Real2, Real3, Policy> const& c)
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{
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//cout << "cparam1 q " << c.param1 // q
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// << ", c.dist z " << c.dist // z
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// << ", c.param2 l " << c.param2 // l
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// << ", quantile (Dist(), c.param1 = q) "
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// << quantile(Dist(), c.param1) //q
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// << endl;
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#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
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BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value);
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BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value);
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#endif
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static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))";
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// Checks on arguments, as not complemented version,
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// Explicit policy.
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typename Dist::value_type q = c.param1;
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if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, c.param3);
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}
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typename Dist::value_type z = c.dist;
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if(!(boost::math::isfinite)(z))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "find_scale z parameter was %1%, but must be finite!", z, c.param3);
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}
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typename Dist::value_type location = c.param2;
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if(!(boost::math::isfinite)(location))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "find_scale location parameter was %1%, but must be finite!", location, c.param3);
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}
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typename Dist::value_type result =
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(c.dist - c.param2) // difference between desired x and current location.
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/ quantile(complement(Dist(), c.param1));
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// ( z - location) / (quantile(complement(Dist(), q))
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if (result <= 0)
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{ // If policy isn't to throw, return the scale <= 0.
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policies::raise_evaluation_error<typename Dist::value_type>(function,
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"Computed scale (%1%) is <= 0!" " Was the complement intended?",
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result, Policy());
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}
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return result;
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} // template <class Dist, class Policy, class Real1, class Real2, class Real3> typename Dist::value_type find_scale
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// So the user can start from the complement q = (1 - p) of the probability p,
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// for example, s = find_scale<normal>(complement(z, q, l));
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template <class Dist, class Real1, class Real2, class Real3>
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inline typename Dist::value_type find_scale(
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complemented3_type<Real1, Real2, Real3> const& c)
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{
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//cout << "cparam1 q " << c.param1 // q
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// << ", c.dist z " << c.dist // z
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// << ", c.param2 l " << c.param2 // l
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// << ", quantile (Dist(), c.param1 = q) "
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// << quantile(Dist(), c.param1) //q
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// << endl;
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#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
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BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value);
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BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value);
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#endif
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static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))";
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// Checks on arguments, as not complemented version,
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// default policy policies::policy<>().
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typename Dist::value_type q = c.param1;
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if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, policies::policy<>());
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}
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typename Dist::value_type z = c.dist;
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if(!(boost::math::isfinite)(z))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "find_scale z parameter was %1%, but must be finite!", z, policies::policy<>());
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}
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typename Dist::value_type location = c.param2;
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if(!(boost::math::isfinite)(location))
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{
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return policies::raise_domain_error<typename Dist::value_type>(
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function, "find_scale location parameter was %1%, but must be finite!", location, policies::policy<>());
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}
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typename Dist::value_type result =
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(z - location) // difference between desired x and current location.
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/ quantile(complement(Dist(), q));
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// ( z - location) / (quantile(complement(Dist(), q))
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if (result <= 0)
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{ // If policy isn't to throw, return the scale <= 0.
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policies::raise_evaluation_error<typename Dist::value_type>(function,
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"Computed scale (%1%) is <= 0!" " Was the complement intended?",
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result, policies::policy<>()); // This is only the default policy - also Want a version with Policy here.
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}
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return result;
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} // template <class Dist, class Real1, class Real2, class Real3> typename Dist::value_type find_scale
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} // namespace boost
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} // namespace math
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#endif // BOOST_STATS_FIND_SCALE_HPP
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