test/std/numerics/rand/rand.dis/rand.dist.bern/rand.dist.bern.negbin/eval.pass.cpp

//===----------------------------------------------------------------------===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
// REQUIRES: long_tests

// <random>

// template<class IntType = int>
// class negative_binomial_distribution

// template<class _URNG> result_type operator()(_URNG& g);

#include <random>
#include <numeric>
#include <vector>
#include <cassert>

#include "test_macros.h"

template <class T>
inline
T
sqr(T x)
{
    return x * x;
}

void
test1()
{
    typedef std::negative_binomial_distribution<> D;
    typedef std::minstd_rand G;
    G g;
    D d(5, .25);
    const int N = 1000000;
    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 (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 = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    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) < 0.02);
}

void
test2()
{
    typedef std::negative_binomial_distribution<> D;
    typedef std::mt19937 G;
    G g;
    D d(30, .03125);
    const int N = 1000000;
    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 (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 = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    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);
}

void
test3()
{
    typedef std::negative_binomial_distribution<> D;
    typedef std::mt19937 G;
    G g;
    D d(40, .25);
    const int N = 1000000;
    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 (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 = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    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);
}

void
test4()
{
    typedef std::negative_binomial_distribution<> D;
    typedef std::mt19937 G;
    G g;
    D d(40, 1);
    const int N = 1000;
    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 (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 = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
//    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
//    double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
    assert(mean == x_mean);
    assert(var == x_var);
}

void
test5()
{
    typedef std::negative_binomial_distribution<> D;
    typedef std::mt19937 G;
    G g;
    D d(400, 0.5);
    const int N = 1000000;
    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 (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 = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    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);
}

void
test6()
{
    typedef std::negative_binomial_distribution<> D;
    typedef std::mt19937 G;
    G g;
    D d(1, 0.05);
    const int N = 1000000;
    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 (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 = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    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);
}

int main(int, char**)
{
    test1();
    test2();
    test3();
    test4();
    test5();
    test6();

  return 0;
}