negative_binomial_distribution Class

Visual Studio 2015

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Generates a negative binomial distribution.

Syntax

class negative_binomial_distribution { public: // types typedef IntType result_type; struct param_type;

```// constructor and reset functions
explicit negative_binomial_distribution(IntType k = 1, double p = 0.5);
explicit negative_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 k() 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 Negative Binomial Distribution discrete probability function. The following table links to articles about individual members.

negative_binomial_distribution::negative_binomial_distribution`negative_binomial_distribution::k``negative_binomial_distribution::param`
`negative_binomial_distribution::operator()``negative_binomial_distribution::p`negative_binomial_distribution::param_type

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

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

Example

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

void test(const int k, 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::negative_binomial_distribution<> distr(k, p);

std::cout << std::endl;
std::cout << "k == " << distr.k() << std::endl;
std::cout << "p == " << distr.p() << 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    k_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 k distribution (where 0 < k): ";
std::cin >> k_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(k_dist, p_dist, samples);
}

```

Output

First run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for k distribution (where 0 `<` k): 1
Enter a double value for p distribution (where 0.0 `<`p `<`= 1.0): .5
Enter an integer value for a sample count: 100

k == 1
p == 0.5
Histogram for 100 samples:
0 :::::::::::::::::::::::::::::::::::::::::::
1 ::::::::::::::::::::::::::::::::
2 ::::::::::::
3 :::::::
4 ::::
5 ::

```

Second run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter an integer value for k distribution (where 0 `<` k): 100
Enter a double value for p distribution (where 0.0 `<` p <= 1.0): .667
Enter an integer value for a sample count: 100

k == 100
p == 0.667
Histogram for 100 samples:
31 ::
32 :
33 ::
34 :
35 ::
37 ::
38 :
39 :
40 ::
41 :::
42 :::
43 :::::
44 :::::
45 ::::
46 ::::::
47 ::::::::
48 :::
49 :::
50 :::::::::
51 :::::::
52 ::
53 :::
54 :::::
56 ::::
58 :
59 :::::
60 ::
61 :
62 ::
64 :
69 ::::

```

Namespace: std

negative_binomial_distribution::negative_binomial_distribution

Constructs the distribution.

```explicit negative_binomial_distribution(IntType k = 1, double p = 0.5);

explicit negative_binomial_distribution(const param_type& parm);

```

Parameters

`k`
The `k` distribution parameter.

`p`
The `p` distribution parameter.

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

Remarks

Precondition: `0.0 < k` and `0.0 < p ≤ 1.0`

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

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.

negative_binomial_distribution::param_type

Stores the parameters of the distribution.

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

Parameters

See parent topic negative_binomial_distribution Class.

Remarks

Precondition: `0.0 < k` 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.