ceph/src/boost/boost/math/statistics/z_test.hpp

   1 //  (C) Copyright Matt Borland 2021.
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #ifndef BOOST_MATH_STATISTICS_Z_TEST_HPP
   7 #define BOOST_MATH_STATISTICS_Z_TEST_HPP
   8
   9 #include <boost/math/distributions/normal.hpp>
  10 #include <boost/math/statistics/univariate_statistics.hpp>
  11 #include <iterator>
  12 #include <type_traits>
  13 #include <utility>
  14 #include <cmath>
  15
  16 namespace boost { namespace math { namespace statistics { namespace detail {
  17
  18 template<typename ReturnType, typename T>
  19 ReturnType one_sample_z_test_impl(T sample_mean, T sample_variance, T sample_size, T assumed_mean)
  20 {
  21     using Real = typename std::tuple_element<0, ReturnType>::type;
  22     using std::sqrt;
  23     using no_promote_policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>>;
  24
  25     Real test_statistic = (sample_mean - assumed_mean) / (sample_variance / sqrt(sample_size));
  26     auto z = boost::math::normal_distribution<Real, no_promote_policy>(sample_size - 1);
  27     Real pvalue;
  28     if(test_statistic > 0)
  29     {
  30         pvalue = 2*boost::math::cdf<Real>(z, -test_statistic);
  31     }
  32     else
  33     {
  34         pvalue = 2*boost::math::cdf<Real>(z, test_statistic);
  35     }
  36
  37     return std::make_pair(test_statistic, pvalue);
  38 }
  39
  40 template<typename ReturnType, typename ForwardIterator>
  41 ReturnType one_sample_z_test_impl(ForwardIterator begin, ForwardIterator end, typename std::iterator_traits<ForwardIterator>::value_type assumed_mean)
  42 {
  43     using Real = typename std::tuple_element<0, ReturnType>::type;
  44     std::pair<Real, Real> temp = mean_and_sample_variance(begin, end);
  45     Real mu = std::get<0>(temp);
  46     Real s_sq = std::get<1>(temp);
  47     return one_sample_z_test_impl<ReturnType>(mu, s_sq, Real(std::distance(begin, end)), Real(assumed_mean));
  48 }
  49
  50 template<typename ReturnType, typename T>
  51 ReturnType two_sample_z_test_impl(T mean_1, T variance_1, T size_1, T mean_2, T variance_2, T size_2)
  52 {
  53     using Real = typename std::tuple_element<0, ReturnType>::type;
  54     using std::sqrt;
  55     using no_promote_policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>>;
  56
  57     Real test_statistic = (mean_1 - mean_2) / sqrt(variance_1/size_1 + variance_2/size_2);
  58     auto z = boost::math::normal_distribution<Real, no_promote_policy>(size_1 + size_2 - 1);
  59     Real pvalue;
  60     if(test_statistic > 0)
  61     {
  62         pvalue = 2*boost::math::cdf<Real>(z, -test_statistic);
  63     }
  64     else
  65     {
  66         pvalue = 2*boost::math::cdf<Real>(z, test_statistic);
  67     }
  68
  69     return std::make_pair(test_statistic, pvalue);
  70 }
  71
  72 template<typename ReturnType, typename ForwardIterator>
  73 ReturnType two_sample_z_test_impl(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2)
  74 {
  75     using Real = typename std::tuple_element<0, ReturnType>::type;
  76     using std::sqrt;
  77     auto n1 = std::distance(begin_1, end_1);
  78     auto n2 = std::distance(begin_2, end_2);
  79
  80     ReturnType temp_1 = mean_and_sample_variance(begin_1, end_1);
  81     Real mean_1 = std::get<0>(temp_1);
  82     Real variance_1 = std::get<1>(temp_1);
  83
  84     ReturnType temp_2 = mean_and_sample_variance(begin_2, end_2);
  85     Real mean_2 = std::get<0>(temp_2);
  86     Real variance_2 = std::get<1>(temp_2);
  87
  88     return two_sample_z_test_impl<ReturnType>(mean_1, variance_1, Real(n1), mean_2, variance_2, Real(n2));
  89 }
  90
  91 } // detail
  92
  93 template<typename Real, typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
  94 inline auto one_sample_z_test(Real sample_mean, Real sample_variance, Real sample_size, Real assumed_mean) -> std::pair<double, double>
  95 {
  96     return detail::one_sample_z_test_impl<std::pair<double, double>>(sample_mean, sample_variance, sample_size, assumed_mean);
  97 }
  98
  99 template<typename Real, typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
 100 inline auto one_sample_z_test(Real sample_mean, Real sample_variance, Real sample_size, Real assumed_mean) -> std::pair<Real, Real>
 101 {
 102     return detail::one_sample_z_test_impl<std::pair<Real, Real>>(sample_mean, sample_variance, sample_size, assumed_mean);
 103 }
 104
 105 template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
 106          typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
 107 inline auto one_sample_z_test(ForwardIterator begin, ForwardIterator end, Real assumed_mean) -> std::pair<double, double>
 108 {
 109     return detail::one_sample_z_test_impl<std::pair<double, double>>(begin, end, assumed_mean);
 110 }
 111
 112 template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
 113          typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
 114 inline auto one_sample_z_test(ForwardIterator begin, ForwardIterator end, Real assumed_mean) -> std::pair<Real, Real>
 115 {
 116     return detail::one_sample_z_test_impl<std::pair<Real, Real>>(begin, end, assumed_mean);
 117 }
 118
 119 template<typename Container, typename Real = typename Container::value_type,
 120          typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
 121 inline auto one_sample_z_test(Container const & v, Real assumed_mean) -> std::pair<double, double>
 122 {
 123     return detail::one_sample_z_test_impl<std::pair<double, double>>(std::begin(v), std::end(v), assumed_mean);
 124 }
 125
 126 template<typename Container, typename Real = typename Container::value_type,
 127          typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
 128 inline auto one_sample_z_test(Container const & v, Real assumed_mean) -> std::pair<Real, Real>
 129 {
 130     return detail::one_sample_z_test_impl<std::pair<Real, Real>>(std::begin(v), std::end(v), assumed_mean);
 131 }
 132
 133 template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
 134          typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
 135 inline auto two_sample_z_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<double, double>
 136 {
 137     return detail::two_sample_z_test_impl<std::pair<double, double>>(begin_1, end_1, begin_2, end_2);
 138 }
 139
 140 template<typename ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
 141          typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
 142 inline auto two_sample_z_test(ForwardIterator begin_1, ForwardIterator end_1, ForwardIterator begin_2, ForwardIterator end_2) -> std::pair<Real, Real>
 143 {
 144     return detail::two_sample_z_test_impl<std::pair<Real, Real>>(begin_1, end_1, begin_2, end_2);
 145 }
 146
 147 template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
 148 inline auto two_sample_z_test(Container const & u, Container const & v) -> std::pair<double, double>
 149 {
 150     return detail::two_sample_z_test_impl<std::pair<double, double>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
 151 }
 152
 153 template<typename Container, typename Real = typename Container::value_type, typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
 154 inline auto two_sample_z_test(Container const & u, Container const & v) -> std::pair<Real, Real>
 155 {
 156     return detail::two_sample_z_test_impl<std::pair<Real, Real>>(std::begin(u), std::end(u), std::begin(v), std::end(v));
 157 }
 158
 159 }}} // boost::math::statistics
 160
 161 #endif // BOOST_MATH_STATISTICS_Z_TEST_HPP