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# chi_squared_distribution Class

Visual Studio 2015

The latest version of this topic can be found at chi_squared_distribution Class.

Generates a chi-squared distribution.

## Syntax

```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::chi_squared_distribution`chi_squared_distribution::n``chi_squared_distribution::param`
`chi_squared_distribution::operator()`chi_squared_distribution::param_type

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

```

Namespace: std

## chi_squared_distribution::chi_squared_distribution

Constructs the distribution.

```explicit chi_squared_distribution(RealType n = 1.0);

explicit chi_squared_distribution(const param_type& parm);

```

### Parameters

`n`
The `n` distribution parameter.

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

### Remarks

Precondition: `0.0 < n`

The first constructor constructs an object whose stored `n` value holds the value `n`.

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.

## chi_squared_distribution::param_type

Stores the parameters of the distribution.

```struct param_type {
typedef chi_squared_distribution<RealType> distribution_type;
param_type(RealType n = 1.0);
RealType n() const;
.....
bool operator==(const param_type& right) const;
bool operator!=(const param_type& right) const;
};

```

### Parameters

See parent topic chi_squared_distribution Class.

### Remarks

Precondition: `0.0 < n`

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.