# negative_binomial_distribution in C++ with Examples

This function is defined in header randomRandom. Negative binomial distribution is Random number distribution that produces integers according to a negative binomial discrete distribution (also known as Pascal distribution), which is described by the following probability mass function.

The value represents the number of failures in a series of independent yes/no trials (each succeeds with probability p), before exactly k successes occur.
Syntax :

template( class IntType = int )
class negative_binomial_distribution


Template Parameter :
IntType : The result type generated by the generator.

Member Types
Member type & Definition

 result_type IntType param_type The type returned by member param

Member functions : public member function

• constructor(): Construct negative binomial distribution
• operstor(): Generate random number
• reset: Reset distribution
• param: Distribution parameters
• min : Minimum value
• max : Maximum value
• Distribution parameters : public member function

• k :Distribution parameter k
• p :Distribution parameter p
• Non-member functions : Function Templates

• operator<< :Insert into output stream
• operator>> :Extract from input stream
• relational operators : Relational operators
• Below program to illustrate the above template

 // 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<int> 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;  }

Output :

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


Below program with distribution parameter of 1 and 20%
Program 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<int> 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;  }

Output :

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



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