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math/test/univariate_statistics_test.cpp
Nick 9e1a5f273a One-sample t-test [CI SKIP]
2019-10-05 15:56:02 -04:00

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/*
* (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();
}
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