negative_binomial_distribution in C++ with Examples
Last Updated :
16 Dec, 2021
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.
P(i|k, p) = \binom{k + i - 1}{i} \cdot p^k \cdot (1 - p)^i
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
- operator(): 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
CPP
// C++ program to illustrate
// negative_binomial_distribution
#include <bits/stdc++.h>
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:
CPP
// C++ program to illustrate
// negative_binomial_distribution
#include <bits/stdc++.h>
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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