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cxx/test/numerics/rand/rand.dis/rand.dist.bern/rand.dist.bern.bin/eval.pass.cpp

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//===----------------------------------------------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
// <random>
// template<class IntType = int>
// class binomial_distribution
// template<class _URNG> result_type operator()(_URNG& g);
#include <iostream>
#include <random>
#include <numeric>
#include <vector>
#include <cassert>
template <class T>
inline
T
sqr(T x)
{
return x * x;
}
int main()
{
{
typedef std::binomial_distribution<> D;
typedef std::minstd_rand G;
G g;
D d(5, .75);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(30, .03125);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(40, .25);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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 < 0.01);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(40, 0);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(40, 1);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(400, 0.5);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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) < 0.01);
assert(std::abs(kurtosis - x_kurtosis) / x_kurtosis < 0.01);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(1, 0.5);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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) < 0.01);
assert(std::abs(kurtosis - x_kurtosis) / x_kurtosis < 0.01);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(0, 0.005);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(0, 0);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
}
{
typedef std::binomial_distribution<> D;
typedef std::mt19937 G;
G g;
D d(0, 1);
const int N = 100000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
assert(d.min() <= v && v <= d.max());
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(),
double(0)) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (int i = 0; i < u.size(); ++i)
{
double d = (u[i] - mean);
double d2 = sqr(d);
var += d2;
skew += d * 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.t() * d.p();
double x_var = x_mean*(1-d.p());
double x_skew = (1-2*d.p()) / std::sqrt(x_var);
double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
assert(mean == x_mean);
assert(var == x_var);
}
}
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