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//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
// <random>
// class bernoulli_distribution
// template<class _URNG> result_type operator()(_URNG& g);
#include <random>
#include <numeric>
#include <vector>
#include <cassert>
#include <cstddef>
template <class T>
inline
T
sqr(T x)
{
return x * x;
}
int main()
{
{
typedef std::bernoulli_distribution D;
typedef std::minstd_rand G;
G g;
D d(.75);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
u.push_back(d(g));
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (std::size_t 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 = d.p();
double x_var = d.p()*(1-d.p());
double x_skew = (1 - 2 * d.p())/std::sqrt(x_var);
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);
}
{
typedef std::bernoulli_distribution D;
typedef std::minstd_rand G;
G g;
D d(.25);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
u.push_back(d(g));
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (std::size_t 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 = d.p();
double x_var = d.p()*(1-d.p());
double x_skew = (1 - 2 * d.p())/std::sqrt(x_var);
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);
}
}
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