std :: poisson_distribution中C++标准库中的错误？

Question

我想我从C++标准库遇到了std :: poisson_distribution的错误行为.

问题:

1. 你能否确认它确实是一个错误而不是我的错误？
2. poisson_distribution函数的标准库代码究竟出了什么问题,假设它确实是一个错误？

细节:

以下C++代码(文件poisson_test.cc)用于生成泊松分布数:

#include <array>
#include <cmath>
#include <iostream>
#include <random>

int main() {
  // The problem turned out to be independent on the engine
  std::mt19937_64 engine;

  // Set fixed seed for easy reproducibility
  // The problem turned out to be independent on seed
  engine.seed(1);
  std::poisson_distribution<int> distribution(157.17);

  for (int i = 0; i < 1E8; i++) {
    const int number = distribution(engine);
    std::cout << number << std::endl;
  }
}

我按如下方式编译此代码:

clang++ -o poisson_test -std=c++11 poisson_test.cc
./poisson_test > mypoisson.txt

以下python脚本用于分析文件mypoisson.txt中的随机数序列:

import numpy as np
import matplotlib.pyplot as plt

def expectation(x, m):
    " Poisson pdf " 
    # Use Ramanujan formula to get ln n!
    lnx = x * np.log(x) - x + 1./6. * np.log(x * (1 + 4*x*(1+2*x))) + 1./2. * np.log(np.pi)
    return np.exp(x*np.log(m) - m - lnx)

data = np.loadtxt('mypoisson.txt', dtype = 'int')

unique, counts = np.unique(data, return_counts = True)
hist = counts.astype(float) / counts.sum()
stat_err = np.sqrt(counts) / counts.sum()
plt.errorbar(unique, hist, yerr = stat_err, fmt = '.', \
             label = 'Poisson generated \n by std::poisson_distribution')
plt.plot(unique, expectation(unique, expected_mean), \
         label = 'expected probability \n density function')
plt.legend()
plt.show()

# Determine bins with statistical significance of deviation larger than 3 sigma
deviation_in_sigma = (hist - expectation(unique, expected_mean)) / stat_err
d = dict((k, v) for k, v in zip(unique, deviation_in_sigma) if np.abs(v) > 3.0)
print d

该脚本生成以下图:

你可以用肉眼看到问题.n = 158时的偏差具有统计显着性,实际上是22σ偏差!

以前的情节的特写镜头.

Answer 1

我的系统设置如下(Debian测试):

libstdc++-7-dev:
  Installed: 7.2.0-16

libc++-dev:
  Installed: 3.5-2

clang:
  Installed: 1:3.8-37

g++:
  Installed: 4:7.2.0-1d1

我可以在使用时确认错误libstdc++:

g++ -o pois_gcc -std=c++11 pois.cpp
clang++ -o pois_clang -std=c++11 -stdlib=libstdc++ pois.cpp
clang++ -o pois_clang_libc -std=c++11 -stdlib=libc++ pois.cpp

结果: