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//===----------------------------------------------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// REQUIRES: long_tests
// <random>
// template<class RealType = double>
// class gamma_distribution
// template<class _URNG> result_type operator()(_URNG& g, const param_type& parm);
#include <random>
#include <cassert>
#include <vector>
#include <numeric>
template <class T>
inline
T
sqr(T x)
{
return x * x;
}
int main()
{
{
typedef std::gamma_distribution<> D;
typedef D::param_type P;
typedef std::mt19937 G;
G g;
D d(0.5, 2);
P p(1, .5);
const int N = 1000000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g, p);
assert(d.min() < v);
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = p.alpha() * p.beta();
double x_var = p.alpha() * sqr(p.beta());
double x_skew = 2 / std::sqrt(p.alpha());
double x_kurtosis = 6 / p.alpha();
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);
}
{
typedef std::gamma_distribution<> D;
typedef D::param_type P;
typedef std::mt19937 G;
G g;
D d(1, .5);
P p(2, 3);
const int N = 1000000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g, p);
assert(d.min() < v);
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = p.alpha() * p.beta();
double x_var = p.alpha() * sqr(p.beta());
double x_skew = 2 / std::sqrt(p.alpha());
double x_kurtosis = 6 / p.alpha();
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);
}
{
typedef std::gamma_distribution<> D;
typedef D::param_type P;
typedef std::mt19937 G;
G g;
D d(2, 3);
P p(.5, 2);
const int N = 1000000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g, p);
assert(d.min() < v);
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = p.alpha() * p.beta();
double x_var = p.alpha() * sqr(p.beta());
double x_skew = 2 / std::sqrt(p.alpha());
double x_kurtosis = 6 / p.alpha();
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);
}
}
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