C++中的negative_binomial_distribution与示例

此函数在标头随机Random中定义。负二项式分布是根据负二项式离散分布(也称为Pascal分布)生成整数的随机数分布，其由以下概率质量函数描述。
$P(i|k, p) = \binom{k + i - 1}{i} \cdot p^k \cdot (1 - p)^i$
该值表示在完全进行k次成功之前，在一系列独立的是/否试验(每次成功均以概率p)中失败的次数。
句法 ：

template( class IntType = int )
class negative_binomial_distribution

模板参数：
IntType：生成器生成的结果类型。

会员类型
会员类型和定义

result_type	IntType
param_type	The type returned by member param

成员职能：公共成员函数

Constructor()：构造负二项分布

operstor()：生成随机数

重置：重置分布

参数：分布参数

min：最小值

max：最大值

分布参数：公共成员函数

k：分布参数k

p：分布参数p

非成员函数：函数模板

运算符<<：插入输出流

运算符>>：从输入流中提取

关系运算符：关系运算符

下面的程序来说明上面的模板

// C++ program to illustrate
// negative_binomial_distribution
#include 
using namespace std;
  
int main()
{
    // number of experiments
    const int exps = 10000;
  
    // maximum number of stars to distribute
    const int numberstars = 100;
  
    // Generator generate numbers based
    // upon a generator function
    default_random_engine generator;
  
    // Aman watches GOT
    // At each episode, there's a 50%
    // chance that john snow will die
    // after how many time he'll be turned
    // away before watching 4 episodes?
    negative_binomial_distribution distribution(4, 0.5);
  
    // initializing an array with size 10
    int p[10] = {};
  
    for (int i = 0; i < exps; ++i) {
        int counting = distribution(generator);
        if (counting < 10)
            ++p[counting];
    }
  
    cout << "Negative binomial distribution with "
         << "( k = 4, p = 0.5 ) :" << endl;
  
    // Printing the sequence stored in an array p
    for (int i = 0; i < 10; ++i)
        cout << i << ": " << string(p[i] * numberstars / exps, '*') << endl;
  
    return 0;
}

输出 ：

Negative binomial distribution with ( k = 4, p = 0.5 ) :
0: *****
1: ************
2: ****************
3: ***************
4: *************
5: **********
6: ********
7: *****
8: ***
9: **

下面的程序，分配参数为1和20％
程式2：

// C++ program to illustrate
// negative_binomial_distribution
#include 
using namespace std;
  
int main()
{
    // number of experiments
    const int exps = 10000;
  
    // maximum number of stars to distribute
    const int numberstars = 100;
  
    // Generator generate numbers based
    // upon a generator function
    default_random_engine generator;
  
    // Aman watches GOT
    // At each episode, there's a
    // 20% chance that john snow will die
    // after how many time he'll be
    // turned away before watching 1 episodes?
    negative_binomial_distribution distribution(1, 0.2);
  
    // initializing an array with size 10
    int p[10] = {};
  
    for (int i = 0; i < exps; ++i) {
        int counting = distribution(generator);
        if (counting < 10)
            ++p[counting];
    }
  
    cout << "Negative binomial distribution with "
         << "( k = 1, p = 0.2 ) :" << endl;
  
    // Printing the sequence stored in an array p
    for (int i = 0; i < 10; ++i)
        cout << i << ": " << string(p[i] * numberstars / exps, '*') << endl;
  
    return 0;
}

输出 ：

Negative binomial distribution with ( k = 1, p = 0.2 ) :
0: *******************
1: ***************
2: ************
3: **********
4: ********
5: ******
6: *****
7: ****
8: ***
9: **

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