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[libc++] Adjust some of the [rand.dist] critical values that are too strict #88669

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Merged
merged 2 commits into from
May 4, 2024
Merged

[libc++] Adjust some of the [rand.dist] critical values that are too strict #88669

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788fc37
Adjust some of the [rand.dist] critical values that are too strict
MattStephanson Apr 14, 2024
7f11755
clang-format
MattStephanson Apr 27, 2024
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8 changes: 4 additions & 4 deletions ...xx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -63,8 +63,8 @@ int main(int, char**)
double x_kurtosis = (6 * sqr(d.p()) - 6 * d.p() + 1)/x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
}
{
typedef std::bernoulli_distribution D;
Expand Down Expand Up @@ -99,8 +99,8 @@ int main(int, char**)
double x_kurtosis = (6 * sqr(d.p()) - 6 * d.p() + 1)/x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
}

return 0;
Expand Down
8 changes: 4 additions & 4 deletions ...t/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bernoulli/eval_param.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -65,8 +65,8 @@ int main(int, char**)
double x_kurtosis = (6 * sqr(p.p()) - 6 * p.p() + 1)/x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
}
{
typedef std::bernoulli_distribution D;
Expand Down Expand Up @@ -103,8 +103,8 @@ int main(int, char**)
double x_kurtosis = (6 * sqr(p.p()) - 6 * p.p() + 1)/x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
}

return 0;
Expand Down
2 changes: 1 addition & 1 deletion .../test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.PR44847.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -163,7 +163,7 @@ int main(int, char**) {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.06);

return 0;
}
12 changes: 6 additions & 6 deletions libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval.pass.cpp
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Expand Up @@ -68,7 +68,7 @@ void test1() {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}

template <class T>
Expand Down Expand Up @@ -109,8 +109,8 @@ void test2() {
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}

template <class T>
Expand Down Expand Up @@ -151,8 +151,8 @@ void test3() {
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.03);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
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Why did you change this test?

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Oops, I was debating changing it to an absolute test because the expected kurtosis is close to zero (-0.017). 2.0 should be the relative bound.

For reference, if you approximate the binomial distribution as normal, you would expect the sample kurtosis to have a standard deviation of $\sqrt{24/N} \approx 0.0155$. That gives a relative 90% confidence interval of $\sqrt{2}\mathrm{erf}^{-1}(0.9)\cdot 0.0155 / 0.017 \approx 1.5$, so I don't think the empirically observed value of 2.0 is unreasonable.

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Can you add something along these lines in the commit message. That give future readers more information why these changes are valid.

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@MattStephanson can you update the commit message? Then the patch is good to land. Thanks.

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@mordante I did update it the last time I force-pushed 788fc37. If it's still missing something, could you please be more specific? Thanks!

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Sorry if I wasn't clear.
When we land this patch the commits will be squashed and merged into one commit. Then we only have the commit message of the review. So what I meant was to edit the top message with the additional information.

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Oh, okay. I think I have it now?

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Yes great! Thanks. I'll land the patch.

assert(std::abs((skew - x_skew) / x_skew) < 0.07);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 2.0);
}

template <class T>
Expand Down Expand Up @@ -292,7 +292,7 @@ void test6() {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs(skew - x_skew) < 0.02);
assert(std::abs(kurtosis - x_kurtosis) < 0.01);
assert(std::abs(kurtosis - x_kurtosis) < 0.03);
}

template <class T>
Expand Down
10 changes: 5 additions & 5 deletions ...xx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.bin/eval_param.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -72,7 +72,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}
{
typedef std::binomial_distribution<> D;
Expand Down Expand Up @@ -113,8 +113,8 @@ int main(int, char**)
double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}
{
typedef std::binomial_distribution<> D;
Expand Down Expand Up @@ -155,8 +155,8 @@ int main(int, char**)
double x_kurtosis = (1-6*p.p()*(1-p.p())) / x_var;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.04);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
assert(std::abs((skew - x_skew) / x_skew) < 0.07);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 2.0);
}

return 0;
Expand Down
12 changes: 6 additions & 6 deletions libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval.pass.cpp
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Expand Up @@ -77,7 +77,7 @@ void test1() {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

template <class T>
Expand Down Expand Up @@ -161,7 +161,7 @@ void test3() {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

template <class T>
Expand Down Expand Up @@ -203,7 +203,7 @@ void test4() {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

template <class T>
Expand Down Expand Up @@ -245,7 +245,7 @@ void test5() {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

template <class T>
Expand Down Expand Up @@ -284,8 +284,8 @@ void test6() {
double x_var = x_mean / d.p();
double x_skew = (2 - d.p()) / std::sqrt((1 - d.p()));
double x_kurtosis = 6 + sqr(d.p()) / (1 - d.p());
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((mean - x_mean) / x_mean) < 0.02);
assert(std::abs((var - x_var) / x_var) < 0.02);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
}
Expand Down
4 changes: 2 additions & 2 deletions ...xx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.geo/eval_param.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -72,7 +72,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}
{
typedef std::geometric_distribution<> D;
Expand Down Expand Up @@ -156,7 +156,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

return 0;
Expand Down
14 changes: 7 additions & 7 deletions libcxx/test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval.pass.cpp
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Expand Up @@ -74,7 +74,7 @@ void test1() {
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

template <class T>
Expand Down Expand Up @@ -115,8 +115,8 @@ void test2() {
double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.1);
}

template <class T>
Expand Down Expand Up @@ -157,8 +157,8 @@ void test3() {
double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}

template <class T>
Expand Down Expand Up @@ -243,8 +243,8 @@ void test5() {
double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.04);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
}

template <class T>
Expand Down
10 changes: 5 additions & 5 deletions ...test/std/numerics/rand/rand.dist/rand.dist.bern/rand.dist.bern.negbin/eval_param.pass.cpp
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Expand Up @@ -72,7 +72,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}
{
typedef std::negative_binomial_distribution<> D;
Expand Down Expand Up @@ -113,8 +113,8 @@ int main(int, char**)
double x_kurtosis = 6. / p.k() + sqr(p.p()) / (p.k() * (1 - p.p()));
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.1);
}
{
typedef std::negative_binomial_distribution<> D;
Expand Down Expand Up @@ -155,8 +155,8 @@ int main(int, char**)
double x_kurtosis = 6. / p.k() + sqr(p.p()) / (p.k() * (1 - p.p()));
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.08);
}

return 0;
Expand Down
6 changes: 3 additions & 3 deletions libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.cauchy/eval.pass.cpp
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Expand Up @@ -45,7 +45,7 @@ int main(int, char**)
u.push_back(d(g));
std::sort(u.begin(), u.end());
for (int i = 0; i < N; ++i)
assert(std::abs(f(u[i], a, b) - double(i)/N) < .001);
assert(std::abs(f(u[i], a, b) - double(i) / N) < .0013);
}
{
typedef std::cauchy_distribution<> D;
Expand All @@ -60,7 +60,7 @@ int main(int, char**)
u.push_back(d(g));
std::sort(u.begin(), u.end());
for (int i = 0; i < N; ++i)
assert(std::abs(f(u[i], a, b) - double(i)/N) < .001);
assert(std::abs(f(u[i], a, b) - double(i) / N) < .0013);
}
{
typedef std::cauchy_distribution<> D;
Expand All @@ -75,7 +75,7 @@ int main(int, char**)
u.push_back(d(g));
std::sort(u.begin(), u.end());
for (int i = 0; i < N; ++i)
assert(std::abs(f(u[i], a, b) - double(i)/N) < .001);
assert(std::abs(f(u[i], a, b) - double(i) / N) < .0013);
}

return 0;
Expand Down
6 changes: 3 additions & 3 deletions libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -70,7 +70,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
}
{
typedef std::chi_squared_distribution<> D;
Expand Down Expand Up @@ -109,7 +109,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}
{
typedef std::chi_squared_distribution<> D;
Expand Down Expand Up @@ -148,7 +148,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

return 0;
Expand Down
6 changes: 3 additions & 3 deletions .../test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval_param.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -72,7 +72,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}
{
typedef std::chi_squared_distribution<> D;
Expand Down Expand Up @@ -113,7 +113,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}
{
typedef std::chi_squared_distribution<> D;
Expand Down Expand Up @@ -154,7 +154,7 @@ int main(int, char**)
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
}

return 0;
Expand Down
18 changes: 9 additions & 9 deletions ...xx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.lognormal/eval.pass.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -70,8 +70,8 @@ test1()
3*std::exp(2*sqr(d.s())) - 6;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.05);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.25);
assert(std::abs((skew - x_skew) / x_skew) < 0.1);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 1.9);
}

void
Expand Down Expand Up @@ -115,7 +115,7 @@ test2()
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
}

void
Expand Down Expand Up @@ -159,7 +159,7 @@ test3()
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.02);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.06);
}

void
Expand Down Expand Up @@ -202,8 +202,8 @@ test4()
3*std::exp(2*sqr(d.s())) - 6;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.02);
assert(std::abs((skew - x_skew) / x_skew) < 0.08);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.4);
assert(std::abs((skew - x_skew) / x_skew) < 0.1);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.5);
}

void
Expand Down Expand Up @@ -245,9 +245,9 @@ test5()
double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) +
3*std::exp(2*sqr(d.s())) - 6;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.04);
assert(std::abs((skew - x_skew) / x_skew) < 0.2);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.7);
assert(std::abs((var - x_var) / x_var) < 0.05);
assert(std::abs((skew - x_skew) / x_skew) < 0.3);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 1.0);
}

int main(int, char**)
Expand Down
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