# binomial_distribution Class

Visual Studio 2015

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Generates a binomial distribution.

## Syntax

```class binomial_distribution
{
public:  // types
typedef IntType result_type;
struct param_type;  // constructors and reset functions
explicit binomial_distribution(IntType t = 1, double p = 0.5);
explicit binomial_distribution(const param_type& parm);
void reset();
// generating functions
template <class URNG>
result_type operator()(URNG& gen);
template <class URNG>
result_type operator()(URNG& gen, const param_type& parm);
// property functions
IntType t() const;
double p() const;
param_type param() const;
void param(const param_type& parm);
result_type min() const;
result_type max() const;
};

```

#### Parameters

`IntType`
The integer result type, defaults to `int`. For possible types, see <random>.

## Remarks

The template class describes a distribution that produces values of a user-specified integral type, or type `int` if none is provided, distributed according to the Binomial Distribution discrete probability function. The following table links to articles about individual members.

binomial_distribution::binomial_distribution`binomial_distribution::t``binomial_distribution::param`
`binomial_distribution::operator()``binomial_distribution::p`binomial_distribution::param_type

The property members `t()` and `p()` return the currently stored distribution parameter values `t` and `p` respectively.

For more information about distribution classes and their members, see <random>.

For detailed information about the binomial distribution discrete probability function, see the Wolfram MathWorld article Binomial Distribution.

## Example

``` // compile with: /EHsc /W4
#include <random>
#include <iostream>
#include <iomanip>
#include <string>
#include <map>

void test(const int t, const double p, const int& s) {

// uncomment to use a non-deterministic seed
//    std::random_device rd;
//    std::mt19937 gen(rd());
std::mt19937 gen(1729);

std::binomial_distribution<> distr(t, p);

std::cout << std::endl;
std::cout << "p == " << distr.p() << std::endl;
std::cout << "t == " << distr.t() << std::endl;

// generate the distribution as a histogram
std::map<int, int> histogram;
for (int i = 0; i < s; ++i) {
++histogram[distr(gen)];
}

// print results
std::cout << "Histogram for " << s << " samples:" << std::endl;
for (const auto& elem : histogram) {
std::cout << std::setw(5) << elem.first << ' ' << std::string(elem.second, ':') << std::endl;
}
std::cout << std::endl;
}

int main()
{
int    t_dist = 1;
double p_dist = 0.5;
int    samples = 100;

std::cout << "Use CTRL-Z to bypass data entry and run using default values." << std::endl;
std::cout << "Enter an integer value for t distribution (where 0 <= t): ";
std::cin >> t_dist;
std::cout << "Enter a double value for p distribution (where 0.0 <= p <= 1.0): ";
std::cin >> p_dist;
std::cout << "Enter an integer value for a sample count: ";
std::cin >> samples;

test(t_dist, p_dist, samples);
}

```

## Output

First run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for t distribution (where 0 <= t): 22
Enter a double value for p distribution (where 0.0 <= p <= 1.0): .25
Enter an integer value for a sample count: 100

p == 0.25
t == 22
Histogram for 100 samples:
1 :
2 ::
3 :::::::::::::
4 ::::::::::::::
5 :::::::::::::::::::::::::
6 ::::::::::::::::::
7 :::::::::::::
8 ::::::
9 ::::::
11 :
12 :

```

Second run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for t distribution (where 0 <= t): 22
Enter a double value for p distribution (where 0.0 <= p <= 1.0): .5
Enter an integer value for a sample count: 100

p == 0.5
t == 22
Histogram for 100 samples:
6 :
7 ::
8 :::::::::
9 ::::::::::
10 ::::::::::::::::
11 :::::::::::::::::::
12 :::::::::::
13 :::::::::::::
14 :::::::::::::::
15 ::
16 ::

```

Third run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for t distribution (where 0 <= t): 22
Enter a double value for p distribution (where 0.0 <= p <= 1.0): .75
Enter an integer value for a sample count: 100

p == 0.75
t == 22
Histogram for 100 samples:
13 ::::
14 :::::::::::
15 :::::::::::::::
16 :::::::::::::::::::::
17 ::::::::::::::
18 :::::::::::::::::
19 :::::::::::
20 ::::::
21 :

```

Namespace: std

## binomial_distribution::binomial_distribution

Constructs the distribution.

```explicit binomial_distribution(IntType t = 1, double p = 0.5);

explicit binomial_distribution(const param_type& parm);

```

### Parameters

`t`
The `t` distribution parameter.

`p`
The `p` distribution parameter.

`parm`
The parameter structure used to construct the distribution.

### Remarks

Precondition: `0 ≤ t` and `0.0 ≤ p ≤ 1.0`

The first constructor constructs an object whose stored `p` value holds the value `p` and whose stored `t` value holds the value `t`.

The second constructor constructs an object whose stored parameters are initialized from `parm`. You can obtain and set the current parameters of an existing distribution by calling the `param()` member function.

For more information and a code example, see binomial_distribution Class.

## binomial_distribution::param_type

Stores all the parameters of the distribution.

```struct param_type {
typedef binomial_distribution<IntType> distribution_type;
param_type(IntType t = 1, double p = 0.5);
IntType t() const;
double p() const;
.....
bool operator==(const param_type& right) const;
bool operator!=(const param_type& right) const;
};

```

### Parameters

See parent topic binomial_distribution Class.

### Remarks

Precondition: `0 ≤ t` and `0.0 ≤ p ≤ 1.0`

This structure can be passed to the distribution's class constructor at instantiation, to the `param()` member function to set the stored parameters of an existing distribution, and to `operator()` to be used in place of the stored parameters.