540 lines
15 KiB
C++
540 lines
15 KiB
C++
//===----------------------------------------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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//
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// REQUIRES: long_tests
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// <random>
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// template<class IntType = int>
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// class binomial_distribution
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// template<class _URNG> result_type operator()(_URNG& g);
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#include <random>
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#include <numeric>
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#include <vector>
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#include <cassert>
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#include "test_macros.h"
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template <class T>
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T sqr(T x) {
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return x * x;
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}
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template <class T>
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void test1() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937_64 G;
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G g;
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D d(5, .75);
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const int N = 1000000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs((skew - x_skew) / x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
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}
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template <class T>
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void test2() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(30, .03125);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs((skew - x_skew) / x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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template <class T>
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void test3() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(40, .25);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs((skew - x_skew) / x_skew) < 0.03);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3);
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}
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template <class T>
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void test4() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(40, 0);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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// In this case:
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// skew computes to 0./0. == nan
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// kurtosis computes to 0./0. == nan
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// x_skew == inf
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// x_kurtosis == inf
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(mean == x_mean);
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assert(var == x_var);
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// assert(skew == x_skew);
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(void)skew; (void)x_skew;
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// assert(kurtosis == x_kurtosis);
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(void)kurtosis; (void)x_kurtosis;
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}
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template <class T>
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void test5() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(40, 1);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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// In this case:
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// skew computes to 0./0. == nan
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// kurtosis computes to 0./0. == nan
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// x_skew == -inf
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// x_kurtosis == inf
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(mean == x_mean);
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assert(var == x_var);
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// assert(skew == x_skew);
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(void)skew; (void)x_skew;
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// assert(kurtosis == x_kurtosis);
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(void)kurtosis; (void)x_kurtosis;
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}
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template <class T>
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void test6() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(127, 0.5);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.02);
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assert(std::abs(kurtosis - x_kurtosis) < 0.01);
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}
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template <class T>
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void test7() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(1, 0.5);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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template <class T>
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void test8() {
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const int N = 100000;
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std::mt19937 gen1;
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std::mt19937 gen2;
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using UnsignedT = typename std::make_unsigned<T>::type;
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std::binomial_distribution<T> dist1(5, 0.1);
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std::binomial_distribution<UnsignedT> dist2(5, 0.1);
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for (int i = 0; i < N; ++i) {
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T r1 = dist1(gen1);
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UnsignedT r2 = dist2(gen2);
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assert(r1 >= 0);
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assert(static_cast<UnsignedT>(r1) == r2);
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}
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}
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template <class T>
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void test9() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(0, 0.005);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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// In this case:
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// skew computes to 0./0. == nan
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// kurtosis computes to 0./0. == nan
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// x_skew == inf
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// x_kurtosis == inf
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(mean == x_mean);
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assert(var == x_var);
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// assert(skew == x_skew);
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(void)skew; (void)x_skew;
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// assert(kurtosis == x_kurtosis);
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(void)kurtosis; (void)x_kurtosis;
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}
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template <class T>
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void test10() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(0, 0);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
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double mean = std::accumulate(u.begin(), u.end(),
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double(0)) / u.size();
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (unsigned i = 0; i < u.size(); ++i)
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{
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double dbl = (u[i] - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= u.size();
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double dev = std::sqrt(var);
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// In this case:
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// skew computes to 0./0. == nan
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// kurtosis computes to 0./0. == nan
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// x_skew == inf
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// x_kurtosis == inf
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skew /= u.size() * dev * var;
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kurtosis /= u.size() * var * var;
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kurtosis -= 3;
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double x_mean = d.t() * d.p();
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double x_var = x_mean*(1-d.p());
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double x_skew = (1-2*d.p()) / std::sqrt(x_var);
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double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var;
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assert(mean == x_mean);
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assert(var == x_var);
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// assert(skew == x_skew);
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(void)skew; (void)x_skew;
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// assert(kurtosis == x_kurtosis);
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(void)kurtosis; (void)x_kurtosis;
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}
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template <class T>
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void test11() {
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typedef std::binomial_distribution<T> D;
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typedef std::mt19937 G;
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G g;
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D d(0, 1);
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const int N = 100000;
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std::vector<typename D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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typename D::result_type v = d(g);
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assert(d.min() <= v && v <= d.max());
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u.push_back(v);
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}
|
|
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);
|
|
// In this case:
|
|
// skew computes to 0./0. == nan
|
|
// kurtosis computes to 0./0. == nan
|
|
// x_skew == -inf
|
|
// x_kurtosis == inf
|
|
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);
|
|
// assert(skew == x_skew);
|
|
(void)skew; (void)x_skew;
|
|
// assert(kurtosis == x_kurtosis);
|
|
(void)kurtosis; (void)x_kurtosis;
|
|
}
|
|
|
|
template <class T>
|
|
void tests() {
|
|
test1<T>();
|
|
test2<T>();
|
|
test3<T>();
|
|
test4<T>();
|
|
test5<T>();
|
|
test6<T>();
|
|
test7<T>();
|
|
test8<T>();
|
|
test9<T>();
|
|
test10<T>();
|
|
test11<T>();
|
|
}
|
|
|
|
int main(int, char**) {
|
|
tests<short>();
|
|
tests<int>();
|
|
tests<long>();
|
|
tests<long long>();
|
|
|
|
tests<unsigned short>();
|
|
tests<unsigned int>();
|
|
tests<unsigned long>();
|
|
tests<unsigned long long>();
|
|
|
|
#if defined(_LIBCPP_VERSION) // extension
|
|
tests<int8_t>();
|
|
tests<uint8_t>();
|
|
#if !defined(TEST_HAS_NO_INT128)
|
|
tests<__int128_t>();
|
|
tests<__uint128_t>();
|
|
#endif
|
|
#endif
|
|
|
|
return 0;
|
|
}
|