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Merged
NAThompson merged 14 commits into from
Sep 4, 2020
Merged

Kolmogorov-Smirnov distribution #422

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945b432
Kolmogorov-Smirnov distribution #421
evanmiller Aug 19, 2020
de347f1
Fix copyright notices [CI SKIP]
evanmiller Aug 19, 2020
59c4da1
Implement skewness for K-S distribution [CI SKIP]
evanmiller Aug 20, 2020
73f0dec
Implement kurtosis for the K-S distribution
evanmiller Aug 21, 2020
8ef4d3f
Fix "0.0" conversion errors with multiprecision types
evanmiller Aug 22, 2020
91fd5f6
Kolmogorov-Smirnov build fixes
evanmiller Aug 22, 2020
fad8917
Kolmogorov-Smirnov needs more BOOST_MATH_STD_USING
evanmiller Aug 22, 2020
ae6c2d8
Kolmogorov-Smirnov build fixes
evanmiller Aug 23, 2020
1599c1d
Require C++11 features for Kolmogorov-Smirnov tests
evanmiller Aug 23, 2020
dafb602
Fix double-to-float warnings with double literals
evanmiller Aug 24, 2020
07791a7
Kolmogorov-Smirnov user documentation [CI SKIP]
evanmiller Aug 30, 2020
c1565d1
Fix code comment (and kick off CI build)
evanmiller Aug 31, 2020
30e325a
Make suggested changes [CI SKIP]
evanmiller Sep 2, 2020
a1fa5e4
Tweak testing logic for K-S mode [CI SKIP]
evanmiller Sep 2, 2020
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Implement skewness for K-S distribution [CI SKIP] 
The third moment integrates nicely with the help of Apery's constant
(zeta_three). Verify the result via quadrature.
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@evanmiller
evanmiller committed Aug 31, 2020
commit 59c4da1dc1d4a643283438be504edcf97094b70e
14 changes: 14 additions & 0 deletions include/boost/math/distributions/kolmogorov_smirnov.hpp
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Expand Up @@ -447,5 +447,19 @@ inline RealType variance(const kolmogorov_smirnov_distribution<RealType, Policy>
return 0.5 * (constants::pi_sqr_div_six<RealType>()
- constants::pi<RealType>() * constants::ln_two<RealType>() * constants::ln_two<RealType>()) / n;
}

template <class RealType, class Policy>
inline RealType skewness(const kolmogorov_smirnov_distribution<RealType, Policy>& dist)
{
static const char* function = "boost::math::skewness(const kolmogorov_smirnov_distribution<%1%>&)";
RealType n = dist.number_of_observations();
RealType error_result = 0;
if(false == detail::check_df(function, n, &error_result, Policy()))
return error_result;
RealType ex3 = 9.0 / 16.0 * constants::root_half_pi<RealType>() * constants::zeta_three<RealType>() / n / sqrt(n);
RealType mean = boost::math::mean(dist);
RealType var = boost::math::variance(dist);
return (ex3 - 3 * mean * var - mean * mean * mean) / var / sqrt(var);
}
}}
#endif
6 changes: 5 additions & 1 deletion test/test_kolmogorov_smirnov.cpp
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Expand Up @@ -59,16 +59,20 @@ void test_spots(RealType T)
BOOST_TEST_CHECK(pdf(dist, mode) >= pdf(dist, mode - 100 * tol));
BOOST_TEST_CHECK(pdf(dist, mode) >= pdf(dist, mode + 100 * tol));

// Test first three moments - pretty well covers the entire distribution
// Test first four moments - pretty well covers the entire distribution
RealType mean = boost::math::mean(dist);
RealType var = variance(dist);
RealType skew = skewness(dist);
quadrature::exp_sinh<RealType> integrator;
auto f_one = [&, dist](RealType t) { return pdf(dist, t); };
auto f_mean = [&, dist](RealType t) { return pdf(dist, t) * t; };
auto f_var = [&, dist, mean](RealType t) { return pdf(dist, t) * (t - mean) * (t - mean); };
auto f_skew = [&, dist, mean, var](RealType t) { return pdf(dist, t)
* (t - mean) * (t - mean) * (t - mean) / var / sqrt(var); };
BOOST_CHECK_CLOSE_FRACTION(integrator.integrate(f_one, eps), RealType(1), tol);
BOOST_CHECK_CLOSE_FRACTION(integrator.integrate(f_mean, eps), mean, tol);
BOOST_CHECK_CLOSE_FRACTION(integrator.integrate(f_var, eps), var, tol);
BOOST_CHECK_CLOSE_FRACTION(integrator.integrate(f_skew, eps), skew, 4*tol);
}

BOOST_AUTO_TEST_CASE( test_main )
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