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#11768: Skewness formula for triangular distribution corrected, tests added and docs updated.

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pabristow
2015-10-29 18:19:46 +00:00
parent 5eb74b83c0
commit 57a71ba5f8
16 changed files with 197 additions and 103 deletions
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126
test/test_triangular.cpp
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@@ -432,46 +432,96 @@ void test_spots(RealType)
boost::math::tools::epsilon<RealType>(),
static_cast<RealType>(boost::math::tools::epsilon<double>())) * 10; // 10 eps as a fraction.
cout << "Tolerance (as fraction) for type " << typeid(RealType).name() << " is " << tolerance << "." << endl;
triangular_distribution<RealType> tridef; // (-1, 0, 1) // default
RealType x = static_cast<RealType>(0.5);
using namespace std; // ADL of std names.
// mean:
BOOST_CHECK_CLOSE_FRACTION(
mean(tridef), static_cast<RealType>(0), tolerance);
// variance:
BOOST_CHECK_CLOSE_FRACTION(
variance(tridef), static_cast<RealType>(0.16666666666666666666666666666666666666666667L), tolerance);
// was 0.0833333333333333333333333333333333333333333L
triangular_distribution<RealType> tridef; // (-1, 0, 1) // Default distribution.
RealType x = static_cast<RealType>(0.5);
using namespace std; // ADL of std names.
// mean:
BOOST_CHECK_CLOSE_FRACTION(
mean(tridef), static_cast<RealType>(0), tolerance);
// variance:
BOOST_CHECK_CLOSE_FRACTION(
variance(tridef), static_cast<RealType>(0.16666666666666666666666666666666666666666667L), tolerance);
// was 0.0833333333333333333333333333333333333333333L
// std deviation:
BOOST_CHECK_CLOSE_FRACTION(
standard_deviation(tridef), sqrt(variance(tridef)), tolerance);
// hazard:
BOOST_CHECK_CLOSE_FRACTION(
hazard(tridef, x), pdf(tridef, x) / cdf(complement(tridef, x)), tolerance);
// cumulative hazard:
BOOST_CHECK_CLOSE_FRACTION(
chf(tridef, x), -log(cdf(complement(tridef, x))), tolerance);
// coefficient_of_variation:
if (mean(tridef) != 0)
{
BOOST_CHECK_CLOSE_FRACTION(
coefficient_of_variation(tridef), standard_deviation(tridef) / mean(tridef), tolerance);
}
// mode:
BOOST_CHECK_CLOSE_FRACTION(
mode(tridef), static_cast<RealType>(0), tolerance);
// skewness:
BOOST_CHECK_CLOSE_FRACTION(
median(tridef), static_cast<RealType>(0), tolerance);
// https://reference.wolfram.com/language/ref/Skewness.html skewness{-1, 0, +1} = 0
// skewness[triangulardistribution{-1, 0, +1}] does not compute a result.
// skewness[triangulardistribution{0, +1}] result == 0
// skewness[normaldistribution{0,1}] result == 0
BOOST_CHECK_EQUAL(
skewness(tridef), static_cast<RealType>(0));
// kurtosis:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(tridef), kurtosis(tridef) - static_cast<RealType>(3L), tolerance);
// kurtosis excess = kurtosis - 3;
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(tridef), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
// std deviation:
BOOST_CHECK_CLOSE_FRACTION(
standard_deviation(tridef), sqrt(variance(tridef)), tolerance);
// hazard:
BOOST_CHECK_CLOSE_FRACTION(
hazard(tridef, x), pdf(tridef, x) / cdf(complement(tridef, x)), tolerance);
// cumulative hazard:
BOOST_CHECK_CLOSE_FRACTION(
chf(tridef, x), -log(cdf(complement(tridef, x))), tolerance);
// coefficient_of_variation:
if (mean(tridef) != 0)
{
BOOST_CHECK_CLOSE_FRACTION(
coefficient_of_variation(tridef), standard_deviation(tridef) / mean(tridef), tolerance);
}
// mode:
BOOST_CHECK_CLOSE_FRACTION(
mode(tridef), static_cast<RealType>(0), tolerance);
// skewness:
BOOST_CHECK_CLOSE_FRACTION(
median(trim12), static_cast<RealType>(-0.13397459621556151), tolerance);
BOOST_CHECK_EQUAL(
skewness(tridef), static_cast<RealType>(0));
// kurtosis:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(tridef), kurtosis(tridef) - static_cast<RealType>(3L), tolerance);
// kurtosis excess = kurtosis - 3;
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(tridef), static_cast<RealType>(-0.6), tolerance); // for all distributions.
triangular_distribution<RealType> tri01(0, 1, 1); // Asymmetric 0, 1, 1 distribution.
RealType x = static_cast<RealType>(0.5);
using namespace std; // ADL of std names.
// mean:
BOOST_CHECK_CLOSE_FRACTION(
mean(tri01), static_cast<RealType>(0.66666666666666666666666666666666666666666666666667L), tolerance);
// variance: N[variance[triangulardistribution{0, 1}, 1], 50]
BOOST_CHECK_CLOSE_FRACTION(
variance(tri01), static_cast<RealType>(0.055555555555555555555555555555555555555555555555556L), tolerance);
// std deviation:
BOOST_CHECK_CLOSE_FRACTION(
standard_deviation(tri01), sqrt(variance(tri01)), tolerance);
// hazard:
BOOST_CHECK_CLOSE_FRACTION(
hazard(tri01, x), pdf(tri01, x) / cdf(complement(tri01, x)), tolerance);
// cumulative hazard:
BOOST_CHECK_CLOSE_FRACTION(
chf(tri01, x), -log(cdf(complement(tri01, x))), tolerance);
// coefficient_of_variation:
if (mean(tri01) != 0)
{
BOOST_CHECK_CLOSE_FRACTION(
coefficient_of_variation(tri01), standard_deviation(tri01) / mean(tri01), tolerance);
}
// mode:
BOOST_CHECK_CLOSE_FRACTION(
mode(tri01), static_cast<RealType>(1), tolerance);
// skewness:
BOOST_CHECK_CLOSE_FRACTION(
median(tri01), static_cast<RealType>(0.70710678118654752440084436210484903928483593768847L), tolerance);
// https://reference.wolfram.com/language/ref/Skewness.html
// N[skewness[triangulardistribution{0, 1}, 1], 50]
BOOST_CHECK_CLOSE_FRACTION(
skewness(tri01), static_cast<RealType>(-0.56568542494923801952067548968387923142786875015078L), tolerance);
// kurtosis:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(tri01), kurtosis(tri01) - static_cast<RealType>(3L), tolerance);
// kurtosis excess = kurtosis - 3;
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(tri01), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
} // tri01 tests
if(std::numeric_limits<RealType>::has_infinity)
{ // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()