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Add unit tests demonstrating that the kurtosis of various continuous distributions is calculated correctly. Add excess_kurtosis to make clear the working definition of kurtosis. [CI SKIP]

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This commit is contained in:
Nick Thompson
2018-12-25 23:00:46 -07:00
parent 53ba643528
commit 4848accb77
3 changed files with 51 additions and 2 deletions
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9
doc/vector_functionals/univariate_statistics.qbk
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@@ -45,6 +45,12 @@ namespace boost{ namespace math{ namespace tools {
template<class ForwardIterator>
auto kurtosis(ForwardIterator first, ForwardIterator last);
template<class Container>
auto excess_kurtosis(Container const & c);
template<class ForwardIterator>
auto excess_kurtosis(ForwardIterator first, ForwardIterator last);
template<class Container>
auto first_four_moments(Container const & c);
@@ -150,7 +156,8 @@ The implementation follows [@https://prod.sandia.gov/techlib-noauth/access-contr
The input data must be forward iterable and must consist of real or integral values.
If the input data is integral, the output is a double precision float.
Note that this is /not/ the excess kurtosis.
If you require the excess kurtosis, subtract 3 from the kurtosis.
If you require the excess kurtosis, use `boost::math::tools::excess_kurtosis`.
This function simply subtracts 3 from the kurtosis, but it makes eminently clear our definition of kurtosis.
[heading First four moments]

12
include/boost/math/tools/univariate_statistics.hpp
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@@ -241,6 +241,18 @@ inline auto kurtosis(Container const & v)
return kurtosis(v.cbegin(), v.cend());
}
template<class ForwardIterator>
auto excess_kurtosis(ForwardIterator first, ForwardIterator last)
{
return kurtosis(first, last) - 3;
}
template<class Container>
inline auto excess_kurtosis(Container const & v)
{
return excess_kurtosis(v.cbegin(), v.cend());
}
// Follows equation 1.5/1.6 of:
// https://prod.sandia.gov/techlib-noauth/access-control.cgi/2008/086212.pdf

32
test/univariate_statistics_test.cpp
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@@ -220,6 +220,35 @@ void test_kurtosis()
kurt = boost::math::tools::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::tools::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::tools::excess_kurtosis(v3);
BOOST_TEST(abs(excess_kurtosis + 6.0/5.0) < 0.2);
// 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.
//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::tools::kurtosis(v3) - 3;
//BOOST_TEST(abs(excess_kurtosis - 6.0) < 0.2);
}
template<class Z>
@@ -427,7 +456,8 @@ int main()
test_kurtosis<float>();
test_kurtosis<double>();
test_kurtosis<long double>();
test_kurtosis<cpp_bin_float_50>();
// Kinda expensive:
//test_kurtosis<cpp_bin_float_50>();
test_first_four_moments<float>();
test_first_four_moments<double>();