Subject: [Boost-commit] svn:boost r76716 - in sandbox/math: . boost boost/math boost/math/distributions
From: pbristow_at_[hidden]
Date: 2012-01-27 12:01:52
Author: pbristow
Date: 2012-01-27 12:01:51 EST (Fri, 27 Jan 2012)
New Revision: 76716
URL: http://svn.boost.org/trac/boost/changeset/76716
Log:
1st commit of skew_normal to boost sandbox, but failures in mode TODO.
Added:
sandbox/math/
sandbox/math/boost/
sandbox/math/boost/math/
sandbox/math/boost/math/distributions/
sandbox/math/boost/math/distributions/skew_normal.hpp (contents, props changed)
Added: sandbox/math/boost/math/distributions/skew_normal.hpp
==============================================================================
--- (empty file)
+++ sandbox/math/boost/math/distributions/skew_normal.hpp 2012-01-27 12:01:51 EST (Fri, 27 Jan 2012)
@@ -0,0 +1,493 @@
+// (C) Benjamin Sobotta 2012
+
+// 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_SKEW_NORMAL_HPP
+#define BOOST_STATS_SKEW_NORMAL_HPP
+
+// http://en.wikipedia.org/wiki/Skew_normal_distribution
+// http://azzalini.stat.unipd.it/SN/
+// Also:
+// Azzalini, A. (1985). "A class of distributions which includes the normal ones".
+// Scand. J. Statist. 12: 171-178.
+
+#include <boost/math/distributions/fwd.hpp> // TODO add skew_normal distribution to fwd.hpp!
+#include <boost/math/special_functions/owens_t.hpp> // Owen's T function
+#include <boost/math/distributions/complement.hpp>
+#include <boost/math/distributions/normal.hpp>
+#include <boost/math/distributions/detail/common_error_handling.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/tools/tuple.hpp>
+#include <boost/math/tools/roots.hpp> // Newton-Raphson
+#include <boost/math/distributions/detail/generic_mode.hpp> // pdf max finder.
+
+#include <utility>
+
+namespace boost{ namespace math{
+
+ namespace detail
+ {
+ template <class RealType, class Policy>
+ inline bool check_skew_normal_shape(
+ const char* function,
+ RealType location,
+ RealType* result,
+ const Policy& pol)
+ {
+ if(!(boost::math::isfinite)(location))
+ {
+ *result =
+ policies::raise_domain_error<RealType>(function,
+ "Shape parameter is %1%, but must be finite!",
+ location, pol);
+ return false;
+ }
+ return true;
+ }
+
+ } // namespace detail
+
+ template <class RealType = double, class Policy = policies::policy<> >
+ class skew_normal_distribution
+ {
+ public:
+ typedef RealType value_type;
+ typedef Policy policy_type;
+
+ skew_normal_distribution(RealType location = 0, RealType scale = 1, RealType shape = 0)
+ : location_(location), scale_(scale), shape_(shape)
+ { // Default is a 'standard' normal distribution N01. (shape=0 results in the normal distribution with no skew)
+ static const char* function = "boost::math::skew_normal_distribution<%1%>::skew_normal_distribution";
+
+ RealType result;
+ detail::check_scale(function, scale, &result, Policy());
+ detail::check_location(function, location, &result, Policy());
+ detail::check_skew_normal_shape(function, shape, &result, Policy());
+ }
+
+ RealType location()const
+ {
+ return location_;
+ }
+
+ RealType scale()const
+ {
+ return scale_;
+ }
+
+ RealType shape()const
+ {
+ return shape_;
+ }
+
+
+ private:
+ //
+ // Data members:
+ //
+ RealType location_; // distribution location.
+ RealType scale_; // distribution scale.
+ RealType shape_; // distribution shape.
+ }; // class skew_normal_distribution
+
+ typedef skew_normal_distribution<double> skew_normal;
+
+ template <class RealType, class Policy>
+ inline const std::pair<RealType, RealType> range(const skew_normal_distribution<RealType, Policy>& /*dist*/)
+ { // Range of permissible values for random variable x.
+ using boost::math::tools::max_value;
+ return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
+ }
+
+ template <class RealType, class Policy>
+ inline const std::pair<RealType, RealType> support(const skew_normal_distribution<RealType, Policy>& /*dist*/)
+ { // 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.
+
+ using boost::math::tools::max_value;
+ return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
+ }
+
+ template <class RealType, class Policy>
+ inline RealType pdf(const skew_normal_distribution<RealType, Policy>& dist, const RealType& x)
+ {
+ const RealType scale = dist.scale();
+ const RealType location = dist.location();
+ const RealType shape = dist.shape();
+
+ static const char* function = "boost::math::pdf(const skew_normal_distribution<%1%>&, %1%)";
+ if((boost::math::isinf)(x))
+ {
+ return 0; // pdf + and - infinity is zero.
+ }
+ // Below produces MSVC 4127 warnings, so the above used instead.
+ //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
+ //{ // pdf + and - infinity is zero.
+ // return 0;
+ //}
+
+ RealType result = 0;
+ if(false == detail::check_scale(function, scale, &result, Policy()))
+ {
+ return result;
+ }
+ if(false == detail::check_location(function, location, &result, Policy()))
+ {
+ return result;
+ }
+ if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+ {
+ return result;
+ }
+ if(false == detail::check_x(function, x, &result, Policy()))
+ {
+ return result;
+ }
+
+ const RealType transformed_x = (x-location)/scale;
+
+ normal_distribution<RealType, Policy> std_normal;
+
+ result = pdf(std_normal, transformed_x) * cdf(std_normal, shape*transformed_x) * 2 / scale;
+
+ return result;
+ } // pdf
+
+ template <class RealType, class Policy>
+ inline RealType cdf(const skew_normal_distribution<RealType, Policy>& dist, const RealType& x)
+ {
+ const RealType scale = dist.scale();
+ const RealType location = dist.location();
+ const RealType shape = dist.shape();
+
+ static const char* function = "boost::math::cdf(const skew_normal_distribution<%1%>&, %1%)";
+ RealType result = 0;
+ if(false == detail::check_scale(function, scale, &result, Policy()))
+ {
+ return result;
+ }
+ if(false == detail::check_location(function, location, &result, Policy()))
+ {
+ return result;
+ }
+ if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+ {
+ return result;
+ }
+ if((boost::math::isinf)(x))
+ {
+ if(x < 0) return 0; // -infinity
+ return 1; // + infinity
+ }
+ // These produce MSVC 4127 warnings, so the above used instead.
+ //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
+ //{ // cdf +infinity is unity.
+ // return 1;
+ //}
+ //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
+ //{ // cdf -infinity is zero.
+ // return 0;
+ //}
+ if(false == detail::check_x(function, x, &result, Policy()))
+ {
+ return result;
+ }
+
+ const RealType transformed_x = (x-location)/scale;
+
+ normal_distribution<RealType, Policy> std_normal;
+
+ result = cdf(std_normal, transformed_x) - owens_t(transformed_x, shape)*2;
+
+ return result;
+ } // cdf
+
+ template <class RealType, class Policy>
+ inline RealType cdf(const complemented2_type<skew_normal_distribution<RealType, Policy>, RealType>& c)
+ {
+ const RealType scale = c.dist.scale();
+ const RealType location = c.dist.location();
+ const RealType shape = c.dist.shape();
+ const RealType x = c.param;
+
+ static const char* function = "boost::math::cdf(const complement(skew_normal_distribution<%1%>&), %1%)";
+
+ if((boost::math::isinf)(x))
+ {
+ if(x < 0) return 1; // cdf complement -infinity is unity.
+ return 0; // cdf complement +infinity is zero
+ }
+ // These produce MSVC 4127 warnings, so the above used instead.
+ //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
+ //{ // cdf complement +infinity is zero.
+ // return 0;
+ //}
+ //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
+ //{ // cdf complement -infinity is unity.
+ // return 1;
+ //}
+ RealType result = 0;
+ if(false == detail::check_scale(function, scale, &result, Policy()))
+ return result;
+ if(false == detail::check_location(function, location, &result, Policy()))
+ return result;
+ if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+ return result;
+ if(false == detail::check_x(function, x, &result, Policy()))
+ return result;
+
+ const RealType transformed_x = (x-location)/scale;
+
+ normal_distribution<RealType, Policy> std_normal;
+
+ result = cdf(complement(std_normal, transformed_x)) + owens_t(transformed_x, shape)*2;
+ return result;
+ } // cdf complement
+
+ template <class RealType, class Policy>
+ inline RealType location(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ return dist.location();
+ }
+
+ template <class RealType, class Policy>
+ inline RealType scale(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ return dist.scale();
+ }
+
+ template <class RealType, class Policy>
+ inline RealType shape(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ return dist.shape();
+ }
+
+ template <class RealType, class Policy>
+ inline RealType mean(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ BOOST_MATH_STD_USING // for ADL of std functions
+
+ using namespace boost::math::constants;
+ // TODO replace by root_two_div_pi<RealType>() when in boost-trunk
+ //static const RealType sqrt_two_over_pi = root_two_div_pi<RealType>(); // = ( 2 / pi ) ^ 0.5
+ static const RealType sqrt_two_over_pi = 7.978845608028654e-001; // = ( 2 / pi ) ^ 0.5
+ const RealType delta = dist.shape() / sqrt(1+dist.shape()*dist.shape());
+
+ return dist.location() + dist.scale()*delta*sqrt_two_over_pi;
+ //return dist.location() + dist.scale() * delta * root_two_div_pi<RealType>();
+ }
+
+ template <class RealType, class Policy>
+ inline RealType variance(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ BOOST_MATH_STD_USING // for ADL of std functions
+
+ using namespace boost::math::constants;
+ //static const RealType two_over_pi = two_div_pi<RealType>(); // = 2 / pi
+ // TODO replace by two_div_pi<RealType>() when in boost-trunk
+ static const RealType two_over_pi = 6.366197723675814e-001; // = 2 / pi
+ const RealType delta = dist.shape() / sqrt(1+dist.shape()*dist.shape());
+ RealType variance = dist.scale()*dist.scale()*(1-two_over_pi*delta*delta);
+ //RealType variance = dist.scale()*dist.scale()*(1-two_div_pi<RealType>() *delta*delta);
+ return variance;
+ }
+
+ /*
+ TODO No closed expression, so use max of pdf.
+ */
+
+ template <class RealType, class Policy>
+ inline RealType mode(const skew_normal_distribution<RealType, Policy>& dist)
+ { // mode.
+ static const char* function = "mode(skew_normal_distribution<%1%> const&)";
+ RealType scale = dist.scale();
+ RealType shape = dist.shape();
+ RealType r;
+ if(!detail::check_scale(
+ function,
+ scale, &r, Policy())
+ ||
+ !detail::check_finite(
+ function,
+ shape,
+ &r,
+ Policy()))
+ return (RealType)r;
+
+ BOOST_MATH_STD_USING
+
+ //RealType m = v < 3 ? 0 : detail::mean(v, l, Policy());
+ //RealType var = v < 4 ? 1 : detail::variance(v, l, Policy());
+
+ RealType guess = (scale < 3) ? 0 : mean(dist);
+ RealType step = (scale < 4) ? 0 : variance(dist); //
+
+ cout << "guess= " << guess << ", step = " << step << endl;
+
+ // TODO problem here in finding lower and upper bounds.
+ // Guess looks reasonable but What should step be?
+
+ return detail::generic_find_mode(
+ dist,
+ guess,
+ function);
+ } // mode
+
+ template <class RealType, class Policy>
+ inline RealType skewness(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ BOOST_MATH_STD_USING // for ADL of std functions
+ // TODO replace by two_div_pi<RealType>() when in boost-trunk
+ // static const RealType two_over_pi = two_div_pi<RealType>(); // = 2 / pi
+ static const RealType two_over_pi = 6.366197723675814e-001; // = 2 / pi
+ static const RealType sqrt_two_over_pi = 7.978845608028654e-001; // = ( 2 / pi ) ^ 0.5
+ static const RealType factor = 4.292036732051034e-001; // = (4-pi)/2
+ const RealType delta = dist.shape() / sqrt(1+dist.shape()*dist.shape());
+
+ return factor * pow(sqrt_two_over_pi * delta, 3) /
+ pow(1 - two_over_pi * delta * delta, static_cast<RealType>(1.5));
+ }
+
+ template <class RealType, class Policy>
+ inline RealType kurtosis(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ return kurtosis_excess(dist)+3;
+ }
+
+ template <class RealType, class Policy>
+ inline RealType kurtosis_excess(const skew_normal_distribution<RealType, Policy>& dist)
+ {
+ BOOST_MATH_STD_USING // for ADL of std functions
+ // TODO replace by two_div_pi<RealType>() etc when in boost-trunk
+ using namespace boost::math::constants;
+
+ static const RealType two_over_pi = 6.366197723675814e-001; // = 2 / pi
+ static const RealType sqrt_two_over_pi = 7.978845608028654e-001; // = ( 2 / pi ) ^ 0.5
+ // static const RealType factor = 2.831853071795862e-001; // = 2*(pi-3) ??? not just 2 * pi_minus_three = 0.141593
+ static const RealType factor = pi_minus_three<RealType>()*static_cast<RealType>(2);
+
+ const RealType delta = dist.shape() / sqrt(1+dist.shape()*dist.shape());
+
+ const RealType x = 1-two_over_pi *delta*delta;
+
+ //return 2 * pi_minus_three<RealType>() * pow(sqrt_two_over_pi * delta, 4) / (x*x) ;
+ return factor * pow(sqrt_two_over_pi * delta, 4) / (x*x) ;
+ }
+
+ namespace detail
+ {
+
+ template <class RealType, class Policy>
+ struct skew_normal_quantile_functor
+ {
+ skew_normal_quantile_functor(const boost::math::skew_normal_distribution<RealType, Policy> dist, RealType const& p)
+ : distribution(dist), prob(p)
+ {
+ }
+
+ boost::math::tuple<RealType, RealType> operator()(RealType const& x)
+ {
+ RealType c = cdf(distribution, x);
+ RealType fx = c - prob; // Difference cdf - value - to minimize.
+ RealType dx = pdf(distribution, x); // pdf is 1st derivative.
+ // return both function evaluation difference f(x) and 1st derivative f'(x).
+ return boost::math::make_tuple(fx, dx);
+ }
+ private:
+ const boost::math::skew_normal_distribution<RealType, Policy> distribution;
+ RealType prob;
+ };
+
+ } // namespace detail
+
+ template <class RealType, class Policy>
+ inline RealType quantile(const skew_normal_distribution<RealType, Policy>& dist, const RealType& p)
+ {
+ const RealType scale = dist.scale();
+ const RealType location = dist.location();
+ const RealType shape = dist.shape();
+
+ static const char* function = "boost::math::quantile(const skew_normal_distribution<%1%>&, %1%)";
+
+ RealType result = 0;
+ if(false == detail::check_scale(function, scale, &result, Policy()))
+ return result;
+ if(false == detail::check_location(function, location, &result, Policy()))
+ return result;
+ if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+ return result;
+ if(false == detail::check_probability(function, p, &result, Policy()))
+ return result;
+
+ // compute initial guess via Cornish-Fisher expansion
+ RealType x = -boost::math::erfc_inv(2 * p, Policy()) * constants::root_two<RealType>();
+
+ // avoid unnecessary computations if there is no skew
+ if(shape != 0)
+ {
+ const RealType skew = skewness(dist);
+ const RealType exk = kurtosis_excess(dist);
+
+ x = x + (x*x-1)*skew/6 + x*(x*x-3)*exk/24 - x*(2*x*x-5)*skew*skew/36;
+ } // if(shape != 0)
+
+ result = standard_deviation(dist)*x+mean(dist);
+
+ // handle special case of non-skew normal distribution
+ if(shape == 0)
+ return result;
+
+ // refine the result by numerically searching the root of (p-cdf)
+
+ const RealType search_min = range(dist).first;
+ const RealType search_max = range(dist).second;
+
+ const int get_digits = policies::digits<RealType, Policy>();// get digits from policy,
+ boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); // and max iterations.
+
+ result = tools::newton_raphson_iterate(detail::skew_normal_quantile_functor<RealType, Policy>(dist, p), result,
+ search_min, search_max, get_digits, m);
+
+ return result;
+ } // quantile
+
+ template <class RealType, class Policy>
+ inline RealType quantile(const complemented2_type<skew_normal_distribution<RealType, Policy>, RealType>& c)
+ {
+ const RealType scale = c.dist.scale();
+ const RealType location = c.dist.location();
+ const RealType shape = c.dist.shape();
+
+ static const char* function = "boost::math::quantile(const complement(skew_normal_distribution<%1%>&), %1%)";
+ RealType result = 0;
+ if(false == detail::check_scale(function, scale, &result, Policy()))
+ return result;
+ if(false == detail::check_location(function, location, &result, Policy()))
+ return result;
+ if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+ return result;
+ RealType q = c.param;
+ if(false == detail::check_probability(function, q, &result, Policy()))
+ return result;
+
+ skew_normal_distribution<RealType, Policy> D(-location, scale, -shape);
+
+ result = -quantile(D, q);
+
+ return result;
+ } // quantile
+
+
+} // namespace math
+} // namespace boost
+
+// 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>
+
+#endif // BOOST_STATS_SKEW_NORMAL_HPP
+
+