cxx/test/numerics/rand/rand.dis/rand.dist.samp/rand.dist.samp.pconst/eval.pass.cpp

//===----------------------------------------------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

// <random>

// template<class RealType = double>
// class piecewise_constant_distribution

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

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

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

int main()
{
    {
        typedef std::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16, 17};
        double p[] = {25, 62.5, 12.5};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16, 17};
        double p[] = {0, 62.5, 12.5};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16, 17};
        double p[] = {25, 0, 12.5};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16, 17};
        double p[] = {25, 62.5, 0};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16, 17};
        double p[] = {25, 0, 0};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16, 17};
        double p[] = {0, 25, 0};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16, 17};
        double p[] = {0, 0, 1};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16};
        double p[] = {75, 25};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16};
        double p[] = {0, 25};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14, 16};
        double p[] = {1, 0};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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::piecewise_constant_distribution<> D;
        typedef std::mt19937_64 G;
        G g;
        double b[] = {10, 14};
        double p[] = {1};
        const size_t Np = sizeof(p) / sizeof(p[0]);
        D d(b, b+Np+1, p);
        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);
        }
        std::vector<double> prob(std::begin(p), std::end(p));
        double s = std::accumulate(prob.begin(), prob.end(), 0.0);
        for (int i = 0; i < prob.size(); ++i)
            prob[i] /= s;
        std::sort(u.begin(), u.end());
        for (int i = 0; i < Np; ++i)
        {
            typedef std::vector<D::result_type>::iterator I;
            I lb = std::lower_bound(u.begin(), u.end(), b[i]);
            I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
            const size_t Ni = ub - lb;
            if (prob[i] == 0)
                assert(Ni == 0);
            else
            {
                assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
                double mean = std::accumulate(lb, ub, 0.0) / Ni;
                double var = 0;
                double skew = 0;
                double kurtosis = 0;
                for (I j = lb; j != ub; ++j)
                {
                    double d = (*j - mean);
                    double d2 = sqr(d);
                    var += d2;
                    skew += d * d2;
                    kurtosis += d2 * d2;
                }
                var /= Ni;
                double dev = std::sqrt(var);
                skew /= Ni * dev * var;
                kurtosis /= Ni * var * var;
                kurtosis -= 3;
                double x_mean = (b[i+1] + b[i]) / 2;
                double x_var = sqr(b[i+1] - b[i]) / 12;
                double x_skew = 0;
                double x_kurtosis = -6./5;
                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);
            }
        }
    }
}