162 lines
7.4 KiB
C++
162 lines
7.4 KiB
C++
// (C) Copyright Matt Borland 2021.
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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_MATH_STATISTICS_Z_TEST_HPP
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#define BOOST_MATH_STATISTICS_Z_TEST_HPP
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#include <boost/math/distributions/normal.hpp>
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#include <boost/math/statistics/univariate_statistics.hpp>
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#include <iterator>
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#include <type_traits>
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#include <utility>
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#include <cmath>
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namespace boost { namespace math { namespace statistics { namespace detail {
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template<typename ReturnType, typename T>
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ReturnType one_sample_z_test_impl(T sample_mean, T sample_variance, T sample_size, T assumed_mean)
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{
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using Real = typename std::tuple_element<0, ReturnType>::type;
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using std::sqrt;
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using no_promote_policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>>;
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Real test_statistic = (sample_mean - assumed_mean) / (sample_variance / sqrt(sample_size));
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auto z = boost::math::normal_distribution<Real, no_promote_policy>(sample_size - 1);
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Real pvalue;
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if(test_statistic > 0)
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{
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pvalue = 2*boost::math::cdf<Real>(z, -test_statistic);
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}
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else
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{
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pvalue = 2*boost::math::cdf<Real>(z, test_statistic);
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}
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return std::make_pair(test_statistic, pvalue);
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}
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template<typename ReturnType, typename ForwardIterator>
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ReturnType one_sample_z_test_impl(ForwardIterator begin, ForwardIterator end, typename std::iterator_traits<ForwardIterator>::value_type assumed_mean)
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{
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using Real = typename std::tuple_element<0, ReturnType>::type;
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std::pair<Real, Real> temp = mean_and_sample_variance(begin, end);
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Real mu = std::get<0>(temp);
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Real s_sq = std::get<1>(temp);
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return one_sample_z_test_impl<ReturnType>(mu, s_sq, Real(std::distance(begin, end)), Real(assumed_mean));
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}
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template<typename ReturnType, typename T>
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ReturnType two_sample_z_test_impl(T mean_1, T variance_1, T size_1, T mean_2, T variance_2, T size_2)
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{
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using Real = typename std::tuple_element<0, ReturnType>::type;
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using std::sqrt;
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using no_promote_policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>>;
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Real test_statistic = (mean_1 - mean_2) / sqrt(variance_1/size_1 + variance_2/size_2);
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auto z = boost::math::normal_distribution<Real, no_promote_policy>(size_1 + size_2 - 1);
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Real pvalue;
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if(test_statistic > 0)
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{
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pvalue = 2*boost::math::cdf<Real>(z, -test_statistic);
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}
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else
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{
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pvalue = 2*boost::math::cdf<Real>(z, test_statistic);
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}
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return std::make_pair(test_statistic, pvalue);
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}
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template<typename ReturnType, typename ForwardIterator>
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ReturnType two_sample_z_test_impl(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2)
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{
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using Real = typename std::tuple_element<0, ReturnType>::type;
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using std::sqrt;
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auto n1 = std::distance(begin_1, end_1);
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auto n2 = std::distance(begin_2, end_2);
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ReturnType temp_1 = mean_and_sample_variance(begin_1, end_1);
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Real mean_1 = std::get<0>(temp_1);
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Real variance_1 = std::get<1>(temp_1);
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ReturnType temp_2 = mean_and_sample_variance(begin_2, end_2);
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Real mean_2 = std::get<0>(temp_2);
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Real variance_2 = std::get<1>(temp_2);
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return two_sample_z_test_impl<ReturnType>(mean_1, variance_1, Real(n1), mean_2, variance_2, Real(n2));
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}
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} // detail
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template<typename Real, typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
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inline auto one_sample_z_test(Real sample_mean, Real sample_variance, Real sample_size, Real assumed_mean) -> std::pair<double, double>
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{
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return detail::one_sample_z_test_impl<std::pair<double, double>>(sample_mean, sample_variance, sample_size, assumed_mean);
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}
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template<typename Real, typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
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inline auto one_sample_z_test(Real sample_mean, Real sample_variance, Real sample_size, Real assumed_mean) -> std::pair<Real, Real>
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{
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return detail::one_sample_z_test_impl<std::pair<Real, Real>>(sample_mean, sample_variance, sample_size, assumed_mean);
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}
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template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
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typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
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inline auto one_sample_z_test(ForwardIterator begin, ForwardIterator end, Real assumed_mean) -> std::pair<double, double>
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{
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return detail::one_sample_z_test_impl<std::pair<double, double>>(begin, end, assumed_mean);
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}
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template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
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typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
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inline auto one_sample_z_test(ForwardIterator begin, ForwardIterator end, Real assumed_mean) -> std::pair<Real, Real>
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{
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return detail::one_sample_z_test_impl<std::pair<Real, Real>>(begin, end, assumed_mean);
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}
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template<typename Container, typename Real = typename Container::value_type,
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typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
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inline auto one_sample_z_test(Container const & v, Real assumed_mean) -> std::pair<double, double>
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{
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return detail::one_sample_z_test_impl<std::pair<double, double>>(std::begin(v), std::end(v), assumed_mean);
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}
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template<typename Container, typename Real = typename Container::value_type,
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typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
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inline auto one_sample_z_test(Container const & v, Real assumed_mean) -> std::pair<Real, Real>
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{
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return detail::one_sample_z_test_impl<std::pair<Real, Real>>(std::begin(v), std::end(v), assumed_mean);
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}
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template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
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typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
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inline auto two_sample_z_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<double, double>
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{
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return detail::two_sample_z_test_impl<std::pair<double, double>>(begin_1, end_1, begin_2, end_2);
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}
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template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
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typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
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inline auto two_sample_z_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<Real, Real>
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{
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return detail::two_sample_z_test_impl<std::pair<Real, Real>>(begin_1, end_1, begin_2, end_2);
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}
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template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
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inline auto two_sample_z_test(Container const & u, Container const & v) -> std::pair<double, double>
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{
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return detail::two_sample_z_test_impl<std::pair<double, double>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
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}
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template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
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inline auto two_sample_z_test(Container const & u, Container const & v) -> std::pair<Real, Real>
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{
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return detail::two_sample_z_test_impl<std::pair<Real, Real>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
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}
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}}} // boost::math::statistics
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#endif // BOOST_MATH_STATISTICS_Z_TEST_HPP
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