Adding upstream version 14.2.21.upstream/14.2.21upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 794 insertions, 0 deletions

diff --git a/src/boost/libs/math/test/univariate_statistics_test.cpp b/src/boost/libs/math/test/univariate_statistics_test.cpp
new file mode 100644
index 00000000..5cee9888
--- /dev/null
+++ b/src/boost/libs/math/test/univariate_statistics_test.cpp
@@ -0,0 +1,794 @@
+/*
+ *  (C) Copyright Nick Thompson 2018.
+ *  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)
+ */
+
+#include <vector>
+#include <array>
+#include <forward_list>
+#include <algorithm>
+#include <random>
+#include <boost/core/lightweight_test.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/statistics/univariate_statistics.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <boost/multiprecision/cpp_complex.hpp>
+
+using boost::multiprecision::cpp_bin_float_50;
+using boost::multiprecision::cpp_complex_50;
+
+/*
+ * Test checklist:
+ * 1) Does it work with multiprecision?
+ * 2) Does it work with .cbegin()/.cend() if the data is not altered?
+ * 3) Does it work with ublas and std::array? (Checking Eigen and Armadillo will make the CI system really unhappy.)
+ * 4) Does it work with std::forward_list if a forward iterator is all that is required?
+ * 5) Does it work with complex data if complex data is sensible?
+ */
+
+ // To stress test, set global_seed = 0, global_size = huge.
+ static const constexpr size_t global_seed = 0;
+ static const constexpr size_t global_size = 128;
+
+template<class T>
+std::vector<T> generate_random_vector(size_t size, size_t seed)
+{
+    if (seed == 0)
+    {
+        std::random_device rd;
+        seed = rd();
+    }
+    std::vector<T> v(size);
+
+    std::mt19937 gen(seed);
+
+    if constexpr (std::is_floating_point<T>::value)
+    {
+        std::normal_distribution<T> dis(0, 1);
+        for (size_t i = 0; i < v.size(); ++i)
+        {
+         v[i] = dis(gen);
+        }
+        return v;
+    }
+    else if constexpr (std::is_integral<T>::value)
+    {
+        // Rescaling by larger than 2 is UB!
+        std::uniform_int_distribution<T> dis(std::numeric_limits<T>::lowest()/2, (std::numeric_limits<T>::max)()/2);
+        for (size_t i = 0; i < v.size(); ++i)
+        {
+         v[i] = dis(gen);
+        }
+        return v;
+    }
+    else if constexpr (boost::is_complex<T>::value)
+    {
+        std::normal_distribution<typename T::value_type> dis(0, 1);
+        for (size_t i = 0; i < v.size(); ++i)
+        {
+            v[i] = {dis(gen), dis(gen)};
+        }
+        return v;
+    }
+    else if constexpr (boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_complex)
+    {
+        std::normal_distribution<long double> dis(0, 1);
+        for (size_t i = 0; i < v.size(); ++i)
+        {
+            v[i] = {dis(gen), dis(gen)};
+        }
+        return v;
+    }
+    else if constexpr (boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_floating_point)
+    {
+        std::normal_distribution<long double> dis(0, 1);
+        for (size_t i = 0; i < v.size(); ++i)
+        {
+            v[i] = dis(gen);
+        }
+        return v;
+    }
+    else
+    {
+        BOOST_ASSERT_MSG(false, "Could not identify type for random vector generation.");
+        return v;
+    }
+}
+
+
+template<class Z>
+void test_integer_mean()
+{
+    double tol = 100*std::numeric_limits<double>::epsilon();
+    std::vector<Z> v{1,2,3,4,5};
+    double mu = boost::math::statistics::mean(v);
+    BOOST_TEST(abs(mu - 3) < tol);
+
+    // Work with std::array?
+    std::array<Z, 5> w{1,2,3,4,5};
+    mu = boost::math::statistics::mean(w);
+    BOOST_TEST(abs(mu - 3) < tol);
+
+    v = generate_random_vector<Z>(global_size, global_seed);
+    Z scale = 2;
+
+    double m1 = scale*boost::math::statistics::mean(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    double m2 = boost::math::statistics::mean(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+}
+
+template<class RandomAccessContainer>
+auto naive_mean(RandomAccessContainer const & v)
+{
+    typename RandomAccessContainer::value_type sum = 0;
+    for (auto & x : v)
+    {
+        sum += x;
+    }
+    return sum/v.size();
+}
+
+template<class Real>
+void test_mean()
+{
+    Real tol = std::numeric_limits<Real>::epsilon();
+    std::vector<Real> v{1,2,3,4,5};
+    Real mu = boost::math::statistics::mean(v.begin(), v.end());
+    BOOST_TEST(abs(mu - 3) < tol);
+
+    // Does range call work?
+    mu = boost::math::statistics::mean(v);
+    BOOST_TEST(abs(mu - 3) < tol);
+
+    // Can we successfully average only part of the vector?
+    mu = boost::math::statistics::mean(v.begin(), v.begin() + 3);
+    BOOST_TEST(abs(mu - 2) < tol);
+
+    // Does it work when we const qualify?
+    mu = boost::math::statistics::mean(v.cbegin(), v.cend());
+    BOOST_TEST(abs(mu - 3) < tol);
+
+    // Does it work for std::array?
+    std::array<Real, 7> u{1,2,3,4,5,6,7};
+    mu = boost::math::statistics::mean(u.begin(), u.end());
+    BOOST_TEST(abs(mu - 4) < tol);
+
+    // Does it work for a forward iterator?
+    std::forward_list<Real> l{1,2,3,4,5,6,7};
+    mu = boost::math::statistics::mean(l.begin(), l.end());
+    BOOST_TEST(abs(mu - 4) < tol);
+
+    // Does it work with ublas vectors?
+    boost::numeric::ublas::vector<Real> w(7);
+    for (size_t i = 0; i < w.size(); ++i)
+    {
+        w[i] = i+1;
+    }
+    mu = boost::math::statistics::mean(w.cbegin(), w.cend());
+    BOOST_TEST(abs(mu - 4) < tol);
+
+    v = generate_random_vector<Real>(global_size, global_seed);
+    Real scale = 2;
+    Real m1 = scale*boost::math::statistics::mean(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    Real m2 = boost::math::statistics::mean(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+
+    // Stress test:
+    for (size_t i = 1; i < 30; ++i)
+    {
+        v = generate_random_vector<Real>(i, 12803);
+        auto naive_ = naive_mean(v);
+        auto higham_ = boost::math::statistics::mean(v);
+        if (abs(higham_ - naive_) >= 100*tol*abs(naive_))
+        {
+            std::cout << std::hexfloat;
+            std::cout << "Terms = " << v.size() << "\n";
+            std::cout << "higham = " << higham_ << "\n";
+            std::cout << "naive_ = " << naive_ << "\n";
+        }
+        BOOST_TEST(abs(higham_ - naive_) < 100*tol*abs(naive_));
+    }
+
+}
+
+template<class Complex>
+void test_complex_mean()
+{
+    typedef typename Complex::value_type Real;
+    Real tol = std::numeric_limits<Real>::epsilon();
+    std::vector<Complex> v{{0,1},{0,2},{0,3},{0,4},{0,5}};
+    auto mu = boost::math::statistics::mean(v.begin(), v.end());
+    BOOST_TEST(abs(mu.imag() - 3) < tol);
+    BOOST_TEST(abs(mu.real()) < tol);
+
+    // Does range work?
+    mu = boost::math::statistics::mean(v);
+    BOOST_TEST(abs(mu.imag() - 3) < tol);
+    BOOST_TEST(abs(mu.real()) < tol);
+}
+
+template<class Real>
+void test_variance()
+{
+    Real tol = std::numeric_limits<Real>::epsilon();
+    std::vector<Real> v{1,1,1,1,1,1};
+    Real sigma_sq = boost::math::statistics::variance(v.begin(), v.end());
+    BOOST_TEST(abs(sigma_sq) < tol);
+
+    sigma_sq = boost::math::statistics::variance(v);
+    BOOST_TEST(abs(sigma_sq) < tol);
+
+    Real s_sq = boost::math::statistics::sample_variance(v);
+    BOOST_TEST(abs(s_sq) < tol);
+
+    std::vector<Real> u{1};
+    sigma_sq = boost::math::statistics::variance(u.cbegin(), u.cend());
+    BOOST_TEST(abs(sigma_sq) < tol);
+
+    std::array<Real, 8> w{0,1,0,1,0,1,0,1};
+    sigma_sq = boost::math::statistics::variance(w.begin(), w.end());
+    BOOST_TEST(abs(sigma_sq - 1.0/4.0) < tol);
+
+    sigma_sq = boost::math::statistics::variance(w);
+    BOOST_TEST(abs(sigma_sq - 1.0/4.0) < tol);
+
+    std::forward_list<Real> l{0,1,0,1,0,1,0,1};
+    sigma_sq = boost::math::statistics::variance(l.begin(), l.end());
+    BOOST_TEST(abs(sigma_sq - 1.0/4.0) < tol);
+
+    v = generate_random_vector<Real>(global_size, global_seed);
+    Real scale = 2;
+    Real m1 = scale*scale*boost::math::statistics::variance(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    Real m2 = boost::math::statistics::variance(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+
+    // Wikipedia example for a variance of N sided die:
+    // https://en.wikipedia.org/wiki/Variance
+    for (size_t j = 16; j < 2048; j *= 2)
+    {
+        v.resize(1024);
+        Real n = v.size();
+        for (size_t i = 0; i < v.size(); ++i)
+        {
+            v[i] = i + 1;
+        }
+
+        sigma_sq = boost::math::statistics::variance(v);
+
+        BOOST_TEST(abs(sigma_sq - (n*n-1)/Real(12)) <= tol*sigma_sq);
+    }
+
+}
+
+template<class Z>
+void test_integer_variance()
+{
+    double tol = std::numeric_limits<double>::epsilon();
+    std::vector<Z> v{1,1,1,1,1,1};
+    double sigma_sq = boost::math::statistics::variance(v);
+    BOOST_TEST(abs(sigma_sq) < tol);
+
+    std::forward_list<Z> l{0,1,0,1,0,1,0,1};
+    sigma_sq = boost::math::statistics::variance(l.begin(), l.end());
+    BOOST_TEST(abs(sigma_sq - 1.0/4.0) < tol);
+
+    v = generate_random_vector<Z>(global_size, global_seed);
+    Z scale = 2;
+    double m1 = scale*scale*boost::math::statistics::variance(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    double m2 = boost::math::statistics::variance(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+}
+
+template<class Z>
+void test_integer_skewness()
+{
+    double tol = std::numeric_limits<double>::epsilon();
+    std::vector<Z> v{1,1,1};
+    double skew = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(skew) < tol);
+
+    // Dataset is symmetric about the mean:
+    v = {1,2,3,4,5};
+    skew = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(skew) < tol);
+
+    v = {0,0,0,0,5};
+    // mu = 1, sigma^2 = 4, sigma = 2, skew = 3/2
+    skew = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(skew - 3.0/2.0) < tol);
+
+    std::forward_list<Z> v2{0,0,0,0,5};
+    skew = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(skew - 3.0/2.0) < tol);
+
+
+    v = generate_random_vector<Z>(global_size, global_seed);
+    Z scale = 2;
+    double m1 = boost::math::statistics::skewness(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    double m2 = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+
+}
+
+template<class Real>
+void test_skewness()
+{
+    Real tol = std::numeric_limits<Real>::epsilon();
+    std::vector<Real> v{1,1,1};
+    Real skew = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(skew) < tol);
+
+    // Dataset is symmetric about the mean:
+    v = {1,2,3,4,5};
+    skew = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(skew) < tol);
+
+    v = {0,0,0,0,5};
+    // mu = 1, sigma^2 = 4, sigma = 2, skew = 3/2
+    skew = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(skew - Real(3)/Real(2)) < tol);
+
+    std::array<Real, 5> w1{0,0,0,0,5};
+    skew = boost::math::statistics::skewness(w1);
+    BOOST_TEST(abs(skew - Real(3)/Real(2)) < tol);
+
+    std::forward_list<Real> w2{0,0,0,0,5};
+    skew = boost::math::statistics::skewness(w2);
+    BOOST_TEST(abs(skew - Real(3)/Real(2)) < tol);
+
+    v = generate_random_vector<Real>(global_size, global_seed);
+    Real scale = 2;
+    Real m1 = boost::math::statistics::skewness(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    Real m2 = boost::math::statistics::skewness(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+}
+
+template<class Real>
+void test_kurtosis()
+{
+    Real tol = std::numeric_limits<Real>::epsilon();
+    std::vector<Real> v{1,1,1};
+    Real kurt = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(kurt) < tol);
+
+    v = {1,2,3,4,5};
+    // mu =1, sigma^2 = 2, kurtosis = 17/10
+    kurt = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(kurt - Real(17)/Real(10)) < tol);
+
+    v = {0,0,0,0,5};
+    // mu = 1, sigma^2 = 4, sigma = 2, skew = 3/2, kurtosis = 13/4
+    kurt = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(kurt - Real(13)/Real(4)) < tol);
+
+    std::array<Real, 5> v1{0,0,0,0,5};
+    kurt = boost::math::statistics::kurtosis(v1);
+    BOOST_TEST(abs(kurt - Real(13)/Real(4)) < tol);
+
+    std::forward_list<Real> v2{0,0,0,0,5};
+    kurt = boost::math::statistics::kurtosis(v2);
+    BOOST_TEST(abs(kurt - Real(13)/Real(4)) < tol);
+
+    std::vector<Real> v3(10000);
+    std::mt19937 gen(42);
+    std::normal_distribution<long double> dis(0, 1);
+    for (size_t i = 0; i < v3.size(); ++i) {
+        v3[i] = dis(gen);
+    }
+    kurt = boost::math::statistics::kurtosis(v3);
+    BOOST_TEST(abs(kurt - 3) < 0.1);
+
+    std::uniform_real_distribution<long double> udis(-1, 3);
+    for (size_t i = 0; i < v3.size(); ++i) {
+        v3[i] = udis(gen);
+    }
+    auto excess_kurtosis = boost::math::statistics::excess_kurtosis(v3);
+    BOOST_TEST(abs(excess_kurtosis + 6.0/5.0) < 0.2);
+
+    v = generate_random_vector<Real>(global_size, global_seed);
+    Real scale = 2;
+    Real m1 = boost::math::statistics::kurtosis(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    Real m2 = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+
+    // This test only passes when there are a large number of samples.
+    // Otherwise, the distribution doesn't generate enough outliers to give,
+    // or generates too many, giving pretty wildly different values of kurtosis on different runs.
+    // However, by kicking up the samples to 1,000,000, I got very close to 6 for the excess kurtosis on every run.
+    // The CI system, however, would die on a million long doubles.
+    //v3.resize(1000000);
+    //std::exponential_distribution<long double> edis(0.1);
+    //for (size_t i = 0; i < v3.size(); ++i) {
+    //    v3[i] = edis(gen);
+    //}
+    //excess_kurtosis = boost::math::statistics::kurtosis(v3) - 3;
+    //BOOST_TEST(abs(excess_kurtosis - 6.0) < 0.2);
+}
+
+template<class Z>
+void test_integer_kurtosis()
+{
+    double tol = std::numeric_limits<double>::epsilon();
+    std::vector<Z> v{1,1,1};
+    double kurt = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(kurt) < tol);
+
+    v = {1,2,3,4,5};
+    // mu =1, sigma^2 = 2, kurtosis = 17/10
+    kurt = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(kurt - 17.0/10.0) < tol);
+
+    v = {0,0,0,0,5};
+    // mu = 1, sigma^2 = 4, sigma = 2, skew = 3/2, kurtosis = 13/4
+    kurt = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(kurt - 13.0/4.0) < tol);
+
+    v = generate_random_vector<Z>(global_size, global_seed);
+    Z scale = 2;
+    double m1 = boost::math::statistics::kurtosis(v);
+    for (auto & x : v)
+    {
+        x *= scale;
+    }
+    double m2 = boost::math::statistics::kurtosis(v);
+    BOOST_TEST(abs(m1 - m2) < tol*abs(m1));
+}
+
+template<class Real>
+void test_first_four_moments()
+{
+    Real tol = 10*std::numeric_limits<Real>::epsilon();
+    std::vector<Real> v{1,1,1};
+    auto [M1_1, M2_1, M3_1, M4_1] = boost::math::statistics::first_four_moments(v);
+    BOOST_TEST(abs(M1_1 - 1) < tol);
+    BOOST_TEST(abs(M2_1) < tol);
+    BOOST_TEST(abs(M3_1) < tol);
+    BOOST_TEST(abs(M4_1) < tol);
+
+    v = {1, 2, 3, 4, 5};
+    auto [M1_2, M2_2, M3_2, M4_2] = boost::math::statistics::first_four_moments(v);
+    BOOST_TEST(abs(M1_2 - 3) < tol);
+    BOOST_TEST(abs(M2_2 - 2) < tol);
+    BOOST_TEST(abs(M3_2) < tol);
+    BOOST_TEST(abs(M4_2 - Real(34)/Real(5)) < tol);
+}
+
+template<class Real>
+void test_median()
+{
+    std::mt19937 g(12);
+    std::vector<Real> v{1,2,3,4,5,6,7};
+
+    Real m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 4);
+
+    std::shuffle(v.begin(), v.end(), g);
+    // Does range call work?
+    m = boost::math::statistics::median(v);
+    BOOST_TEST_EQ(m, 4);
+
+    v = {1,2,3,3,4,5};
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 3);
+    std::shuffle(v.begin(), v.end(), g);
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 3);
+
+    v = {1};
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 1);
+
+    v = {1,1};
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 1);
+
+    v = {2,4};
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 3);
+
+    v = {1,1,1};
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 1);
+
+    v = {1,2,3};
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 2);
+    std::shuffle(v.begin(), v.end(), g);
+    m = boost::math::statistics::median(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 2);
+
+    // Does it work with std::array?
+    std::array<Real, 3> w{1,2,3};
+    m = boost::math::statistics::median(w);
+    BOOST_TEST_EQ(m, 2);
+
+    // Does it work with ublas?
+    boost::numeric::ublas::vector<Real> w1(3);
+    w1[0] = 1;
+    w1[1] = 2;
+    w1[2] = 3;
+    m = boost::math::statistics::median(w);
+    BOOST_TEST_EQ(m, 2);
+}
+
+template<class Real>
+void test_median_absolute_deviation()
+{
+    std::vector<Real> v{-1, 2, -3, 4, -5, 6, -7};
+
+    Real m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 4);
+
+    std::mt19937 g(12);
+    std::shuffle(v.begin(), v.end(), g);
+    m = boost::math::statistics::median_absolute_deviation(v, 0);
+    BOOST_TEST_EQ(m, 4);
+
+    v = {1, -2, -3, 3, -4, -5};
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 3);
+    std::shuffle(v.begin(), v.end(), g);
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 3);
+
+    v = {-1};
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 1);
+
+    v = {-1, 1};
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 1);
+    // The median is zero, so coincides with the default:
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end());
+    BOOST_TEST_EQ(m, 1);
+
+    m = boost::math::statistics::median_absolute_deviation(v);
+    BOOST_TEST_EQ(m, 1);
+
+
+    v = {2, -4};
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 3);
+
+    v = {1, -1, 1};
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 1);
+
+    v = {1, 2, -3};
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 2);
+    std::shuffle(v.begin(), v.end(), g);
+    m = boost::math::statistics::median_absolute_deviation(v.begin(), v.end(), 0);
+    BOOST_TEST_EQ(m, 2);
+
+    std::array<Real, 3> w{1, 2, -3};
+    m = boost::math::statistics::median_absolute_deviation(w, 0);
+    BOOST_TEST_EQ(m, 2);
+
+    // boost.ublas vector?
+    boost::numeric::ublas::vector<Real> u(6);
+    u[0] = 1;
+    u[1] = 2;
+    u[2] = -3;
+    u[3] = 1;
+    u[4] = 2;
+    u[5] = -3;
+    m = boost::math::statistics::median_absolute_deviation(u, 0);
+    BOOST_TEST_EQ(m, 2);
+}
+
+
+template<class Real>
+void test_sample_gini_coefficient()
+{
+    Real tol = std::numeric_limits<Real>::epsilon();
+    std::vector<Real> v{1,0,0};
+    Real gini = boost::math::statistics::sample_gini_coefficient(v.begin(), v.end());
+    BOOST_TEST(abs(gini - 1) < tol);
+
+    gini = boost::math::statistics::sample_gini_coefficient(v);
+    BOOST_TEST(abs(gini - 1) < tol);
+
+    v[0] = 1;
+    v[1] = 1;
+    v[2] = 1;
+    gini = boost::math::statistics::sample_gini_coefficient(v.begin(), v.end());
+    BOOST_TEST(abs(gini) < tol);
+
+    v[0] = 0;
+    v[1] = 0;
+    v[2] = 0;
+    gini = boost::math::statistics::sample_gini_coefficient(v.begin(), v.end());
+    BOOST_TEST(abs(gini) < tol);
+
+    std::array<Real, 3> w{0,0,0};
+    gini = boost::math::statistics::sample_gini_coefficient(w);
+    BOOST_TEST(abs(gini) < tol);
+}
+
+
+template<class Real>
+void test_gini_coefficient()
+{
+    Real tol = std::numeric_limits<Real>::epsilon();
+    std::vector<Real> v{1,0,0};
+    Real gini = boost::math::statistics::gini_coefficient(v.begin(), v.end());
+    Real expected = Real(2)/Real(3);
+    BOOST_TEST(abs(gini - expected) < tol);
+
+    gini = boost::math::statistics::gini_coefficient(v);
+    BOOST_TEST(abs(gini - expected) < tol);
+
+    v[0] = 1;
+    v[1] = 1;
+    v[2] = 1;
+    gini = boost::math::statistics::gini_coefficient(v.begin(), v.end());
+    BOOST_TEST(abs(gini) < tol);
+
+    v[0] = 0;
+    v[1] = 0;
+    v[2] = 0;
+    gini = boost::math::statistics::gini_coefficient(v.begin(), v.end());
+    BOOST_TEST(abs(gini) < tol);
+
+    std::array<Real, 3> w{0,0,0};
+    gini = boost::math::statistics::gini_coefficient(w);
+    BOOST_TEST(abs(gini) < tol);
+
+    boost::numeric::ublas::vector<Real> w1(3);
+    w1[0] = 1;
+    w1[1] = 1;
+    w1[2] = 1;
+    gini = boost::math::statistics::gini_coefficient(w1);
+    BOOST_TEST(abs(gini) < tol);
+
+    std::mt19937 gen(18);
+    // Gini coefficient for a uniform distribution is (b-a)/(3*(b+a));
+    std::uniform_real_distribution<long double> dis(0, 3);
+    expected = (dis.b() - dis.a())/(3*(dis.b()+ dis.a()));
+    v.resize(1024);
+    for(size_t i = 0; i < v.size(); ++i)
+    {
+        v[i] = dis(gen);
+    }
+    gini = boost::math::statistics::gini_coefficient(v);
+    BOOST_TEST(abs(gini - expected) < 0.01);
+
+}
+
+template<class Z>
+void test_integer_gini_coefficient()
+{
+    double tol = std::numeric_limits<double>::epsilon();
+    std::vector<Z> v{1,0,0};
+    double gini = boost::math::statistics::gini_coefficient(v.begin(), v.end());
+    double expected = 2.0/3.0;
+    BOOST_TEST(abs(gini - expected) < tol);
+
+    gini = boost::math::statistics::gini_coefficient(v);
+    BOOST_TEST(abs(gini - expected) < tol);
+
+    v[0] = 1;
+    v[1] = 1;
+    v[2] = 1;
+    gini = boost::math::statistics::gini_coefficient(v.begin(), v.end());
+    BOOST_TEST(abs(gini) < tol);
+
+    v[0] = 0;
+    v[1] = 0;
+    v[2] = 0;
+    gini = boost::math::statistics::gini_coefficient(v.begin(), v.end());
+    BOOST_TEST(abs(gini) < tol);
+
+    std::array<Z, 3> w{0,0,0};
+    gini = boost::math::statistics::gini_coefficient(w);
+    BOOST_TEST(abs(gini) < tol);
+
+    boost::numeric::ublas::vector<Z> w1(3);
+    w1[0] = 1;
+    w1[1] = 1;
+    w1[2] = 1;
+    gini = boost::math::statistics::gini_coefficient(w1);
+    BOOST_TEST(abs(gini) < tol);
+}
+
+int main()
+{
+    test_mean<float>();
+    test_mean<double>();
+    test_mean<long double>();
+    test_mean<cpp_bin_float_50>();
+
+    test_integer_mean<unsigned>();
+    test_integer_mean<int>();
+
+    test_complex_mean<std::complex<float>>();
+    test_complex_mean<cpp_complex_50>();
+
+    test_variance<float>();
+    test_variance<double>();
+    test_variance<long double>();
+    test_variance<cpp_bin_float_50>();
+
+    test_integer_variance<int>();
+    test_integer_variance<unsigned>();
+
+    test_skewness<float>();
+    test_skewness<double>();
+    test_skewness<long double>();
+    test_skewness<cpp_bin_float_50>();
+
+    test_integer_skewness<int>();
+    test_integer_skewness<unsigned>();
+
+    test_first_four_moments<float>();
+    test_first_four_moments<double>();
+    test_first_four_moments<long double>();
+    test_first_four_moments<cpp_bin_float_50>();
+
+    test_kurtosis<float>();
+    test_kurtosis<double>();
+    test_kurtosis<long double>();
+    // Kinda expensive:
+    //test_kurtosis<cpp_bin_float_50>();
+
+    test_integer_kurtosis<int>();
+    test_integer_kurtosis<unsigned>();
+
+    test_median<float>();
+    test_median<double>();
+    test_median<long double>();
+    test_median<cpp_bin_float_50>();
+    test_median<int>();
+
+    test_median_absolute_deviation<float>();
+    test_median_absolute_deviation<double>();
+    test_median_absolute_deviation<long double>();
+    test_median_absolute_deviation<cpp_bin_float_50>();
+
+    test_gini_coefficient<float>();
+    test_gini_coefficient<double>();
+    test_gini_coefficient<long double>();
+    test_gini_coefficient<cpp_bin_float_50>();
+
+    test_integer_gini_coefficient<unsigned>();
+    test_integer_gini_coefficient<int>();
+
+    test_sample_gini_coefficient<float>();
+    test_sample_gini_coefficient<double>();
+    test_sample_gini_coefficient<long double>();
+    test_sample_gini_coefficient<cpp_bin_float_50>();
+
+    return boost::report_errors();
+}