boost/math/distributions/find_scale.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_SCALE_HPP
#define BOOST_STATS_FIND_SCALE_HPP
#include <boost/math/distributions/fwd.hpp> // for all distribution signatures.
#include <boost/math/distributions/complement.hpp>
#include <boost/math/policies/policy.hpp>
// using boost::math::policies::policy;
#include <boost/math/tools/traits.hpp>
#include <boost/static_assert.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
#include <boost/math/policies/error_handling.hpp>
// 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),
// distributions that have scale.
// BOOST_STATIC_ASSERTs, see below, are used to enforce this.
template <class Dist, class Policy>
inline
typename Dist::value_type find_scale( // 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 weight 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 location, // location parameter, for example, normal distribution mean.
const Policy& pol
)
{
#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value);
BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value);
#endif
static const char* function = "boost::math::find_scale<Dist, Policy>(%1%, %1%, %1%, Policy)";
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, "find_scale z parameter was %1%, but must be finite!", z, pol);
}
if(!(boost::math::isfinite)(location))
{
return policies::raise_domain_error<typename Dist::value_type>(
function, "find_scale location parameter was %1%, but must be finite!", location, pol);
}
//cout << "z " << z << ", p " << p << ", quantile(Dist(), p) "
//<< quantile(Dist(), p) << ", z - mean " << z - location
//<<", sd " << (z - location) / quantile(Dist(), p) << endl;
//quantile(N01, 0.001) -3.09023
//quantile(N01, 0.01) -2.32635
//quantile(N01, 0.05) -1.64485
//quantile(N01, 0.333333) -0.430728
//quantile(N01, 0.5) 0
//quantile(N01, 0.666667) 0.430728
//quantile(N01, 0.9) 1.28155
//quantile(N01, 0.95) 1.64485
//quantile(N01, 0.99) 2.32635
//quantile(N01, 0.999) 3.09023
typename Dist::value_type result =
(z - location) // difference between desired x and current location.
/ quantile(Dist(), p); // standard distribution.
if (result <= 0)
{ // If policy isn't to throw, return the scale <= 0.
policies::raise_evaluation_error<typename Dist::value_type>(function,
"Computed scale (%1%) is <= 0!" " Was the complement intended?",
result, Policy());
}
return result;
} // template <class Dist, class Policy> find_scale
template <class Dist>
inline // with default policy.
typename Dist::value_type find_scale( // 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 location) // location parameter, for example, mean.
{ // Forward to find_scale using the default policy.
return (find_scale<Dist>(z, p, location, policies::policy<>()));
} // find_scale
template <class Dist, class Real1, class Real2, class Real3, class Policy>
inline typename Dist::value_type find_scale(
complemented4_type<Real1, Real2, Real3, Policy> const& c)
{
//cout << "cparam1 q " << c.param1 // q
// << ", c.dist z " << c.dist // z
// << ", c.param2 l " << c.param2 // l
// << ", quantile (Dist(), c.param1 = q) "
// << quantile(Dist(), c.param1) //q
// << endl;
#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value);
BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value);
#endif
static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))";
// Checks on arguments, as not complemented version,
// Explicit policy.
typename Dist::value_type q = c.param1;
if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1))
{
return policies::raise_domain_error<typename Dist::value_type>(
function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, c.param3);
}
typename Dist::value_type z = c.dist;
if(!(boost::math::isfinite)(z))
{
return policies::raise_domain_error<typename Dist::value_type>(
function, "find_scale z parameter was %1%, but must be finite!", z, c.param3);
}
typename Dist::value_type location = c.param2;
if(!(boost::math::isfinite)(location))
{
return policies::raise_domain_error<typename Dist::value_type>(
function, "find_scale location parameter was %1%, but must be finite!", location, c.param3);
}
typename Dist::value_type result =
(c.dist - c.param2) // difference between desired x and current location.
/ quantile(complement(Dist(), c.param1));
// ( z - location) / (quantile(complement(Dist(), q))
if (result <= 0)
{ // If policy isn't to throw, return the scale <= 0.
policies::raise_evaluation_error<typename Dist::value_type>(function,
"Computed scale (%1%) is <= 0!" " Was the complement intended?",
result, Policy());
}
return result;
} // template <class Dist, class Policy, class Real1, class Real2, class Real3> typename Dist::value_type find_scale
// So the user can start from the complement q = (1 - p) of the probability p,
// for example, s = find_scale<normal>(complement(z, q, l));
template <class Dist, class Real1, class Real2, class Real3>
inline typename Dist::value_type find_scale(
complemented3_type<Real1, Real2, Real3> const& c)
{
//cout << "cparam1 q " << c.param1 // q
// << ", c.dist z " << c.dist // z
// << ", c.param2 l " << c.param2 // l
// << ", quantile (Dist(), c.param1 = q) "
// << quantile(Dist(), c.param1) //q
// << endl;
#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value);
BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value);
#endif
static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))";
// Checks on arguments, as not complemented version,
// default policy policies::policy<>().
typename Dist::value_type q = c.param1;
if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1))
{
return policies::raise_domain_error<typename Dist::value_type>(
function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, policies::policy<>());
}
typename Dist::value_type z = c.dist;
if(!(boost::math::isfinite)(z))
{
return policies::raise_domain_error<typename Dist::value_type>(
function, "find_scale z parameter was %1%, but must be finite!", z, policies::policy<>());
}
typename Dist::value_type location = c.param2;
if(!(boost::math::isfinite)(location))
{
return policies::raise_domain_error<typename Dist::value_type>(
function, "find_scale location parameter was %1%, but must be finite!", location, policies::policy<>());
}
typename Dist::value_type result =
(z - location) // difference between desired x and current location.
/ quantile(complement(Dist(), q));
// ( z - location) / (quantile(complement(Dist(), q))
if (result <= 0)
{ // If policy isn't to throw, return the scale <= 0.
policies::raise_evaluation_error<typename Dist::value_type>(function,
"Computed scale (%1%) is <= 0!" " Was the complement intended?",
result, policies::policy<>()); // This is only the default policy - also Want a version with Policy here.
}
return result;
} // template <class Dist, class Real1, class Real2, class Real3> typename Dist::value_type find_scale
} // namespace boost
} // namespace math
#endif // BOOST_STATS_FIND_SCALE_HPP