# chi_squared_distribution Class

Visual Studio 2013

Generates a chi-squared distribution.

```template<class RealType = double>
class chi_squared_distribution
{
public:
// types
typedef RealType result_type;
struct param_type;
// constructor and reset functions
explicit chi_squared_distribution(RealType n = 1);
explicit chi_squared_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
RealType n() const;
param_type param() const;
void param(const param_type& parm);
result_type min() const;
result_type max() const;
};
```

## Parameters

RealType

The floating-point result type, defaults to double. For possible types, see <random>.

## Remarks

The template class describes a distribution that produces values of a user-specified integral type, or type double if none is provided, distributed according to the Chi-Squared Distribution. The following table links to articles about individual members.

 chi_squared_distribution::n chi_squared_distribution::param chi_squared_distribution::operator()

The property function n() returns the value for the stored distribution parameter n.

For detailed information about the chi-squared distribution, see the Wolfram MathWorld article Chi-Squared Distribution.

## Example

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

void test(const double n, const int s) {

// uncomment to use a non-deterministic generator
//    std::random_device gen;
std::mt19937 gen(1701);

std::chi_squared_distribution<> distr(n);

std::cout << std::endl;
std::cout << "min() == " << distr.min() << std::endl;
std::cout << "max() == " << distr.max() << std::endl;
std::cout << "n() == " << std::fixed << std::setw(11) << std::setprecision(10) << distr.n() << std::endl;

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

// print results
std::cout << "Distribution for " << s << " samples:" << std::endl;
int counter = 0;
for (const auto& elem : histogram) {
std::cout << std::fixed << std::setw(11) << ++counter << ": "
<< std::setw(14) << std::setprecision(10) << elem.first << std::endl;
}
std::cout << std::endl;
}

int main()
{
double n_dist = 0.5;
int samples = 10;

std::cout << "Use CTRL-Z to bypass data entry and run using default values." << std::endl;
std::cout << "Enter a floating point value for the \'n\' distribution parameter (must be greater than zero): ";
std::cin >> n_dist;
std::cout << "Enter an integer value for the sample count: ";
std::cin >> samples;

test(n_dist, samples);
}
```

## Output

First run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter a floating point value for the 'n' distribution parameter (must be greater than zero): .5
Enter an integer value for the sample count: 10

min() == 4.94066e-324
max() == 1.79769e+308
n() == 0.5000000000
Distribution for 10 samples:
1:   0.0007625595
2:   0.0016895062
3:   0.0058683478
4:   0.0189647765
5:   0.0556619371
6:   0.1448191353
7:   0.1448245325
8:   0.1903494379
9:   0.9267525768
10:   1.5429743723
```

Second run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter a floating point value for the 'n' distribution parameter (must be greater than zero): .3333
Enter an integer value for the sample count: 10

min() == 4.94066e-324
max() == 1.79769e+308
n() == 0.3333000000
Distribution for 10 samples:
1:   0.0000148725
2:   0.0000490528
3:   0.0003175988
4:   0.0018454535
5:   0.0092808795
6:   0.0389540735
7:   0.0389562514
8:   0.0587028468
9:   0.6183666639
10:   1.3552086624
```

Third run:

```Use CTRL-Z to bypass data entry and run using default values.
Enter a floating point value for the 'n' distribution parameter (must be greater than zero): 1000
Enter an integer value for the sample count: 10

min() == 4.94066e-324
max() == 1.79769e+308
n() == 1000.0000000000
Distribution for 10 samples:
1: 958.5284624473
2: 958.7882787809
3: 963.0667684792
4: 987.9638091514
5: 1016.2433493745
6: 1021.9337111110
7: 1021.9723046240
8: 1035.7622110505
9: 1043.8725156645
10: 1054.7051509381
```