cauchy_distribution Class

Generates a Cauchy distribution.

template<class RealType = double>
class cauchy_distribution
{
public:
    // types
    typedef RealType result_type;
    struct param_type;
    // constructor and reset functions
    explicit cauchy_distribution(RealType a = 0.0, RealType b = 1.0);
    explicit cauchy_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 a() const;
    RealType b() 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 Cauchy Distribution. The following table links to articles about individual members.

cauchy_distribution::cauchy_distribution	cauchy_distribution::a	cauchy_distribution::param
cauchy_distribution::operator()	cauchy_distribution::b	cauchy_distribution::param_type

The property functions a() and b() return their respective values for stored distribution parameters a and b.

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

For detailed information about the cauchy distribution, see the Wolfram MathWorld article Cauchy Distribution.

Example

 

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

void test(const double a, const double b, const int s) {

    // uncomment to use a non-deterministic generator
    //    std::random_device gen;

    std::mt19937 gen(1701);

    std::cauchy_distribution<> distr(a, b);

    std::cout << std::endl;
    std::cout << "min() == " << distr.min() << std::endl;
    std::cout << "max() == " << distr.max() << std::endl;
    std::cout << "a() == " << std::fixed << std::setw(11) << std::setprecision(10) << distr.a() << std::endl;
    std::cout << "b() == " << std::fixed << std::setw(11) << std::setprecision(10) << distr.b() << 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 a_dist = 0.0;
    double b_dist = 1;

    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 'a' distribution parameter: ";
    std::cin >> a_dist;
    std::cout << "Enter a floating point value for the 'b' distribution parameter (must be greater than zero): ";
    std::cin >> b_dist;
    std::cout << "Enter an integer value for the sample count: ";
    std::cin >> samples;

    test(a_dist, b_dist, samples);
}

Output

First run:

Use CTRL-Z to bypass data entry and run using default values.
Enter a floating point value for the 'a' distribution parameter: 0
Enter a floating point value for the 'b' distribution parameter (must be greater than zero): 1
Enter an integer value for the sample count: 10

min() == -1.79769e+308
max() == 1.79769e+308
a() == 0.0000000000
b() == 1.0000000000
Distribution for 10 samples:
          1:  -3.4650392984
          2:  -2.6369564174
          3:  -0.0786978867
          4:  -0.0609632093
          5:   0.0589387400
          6:   0.0589539764
          7:   0.1004592006
          8:   1.0965724260
          9:   1.4389408122
         10:   2.5253154706

Second run:

Use CTRL-Z to bypass data entry and run using default values.
Enter a floating point value for the 'a' distribution parameter: 0
Enter a floating point value for the 'b' distribution parameter (must be greater than zero): 10
Enter an integer value for the sample count: 10

min() == -1.79769e+308
max() == 1.79769e+308
a() == 0.0000000000
b() == 10.0000000000
Distribution for 10 samples:
          1: -34.6503929840
          2: -26.3695641736
          3:  -0.7869788674
          4:  -0.6096320926
          5:   0.5893873999
          6:   0.5895397637
          7:   1.0045920062
          8:  10.9657242597
          9:  14.3894081218
         10:  25.2531547063

Third run:

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

min() == -1.79769e+308
max() == 1.79769e+308
a() == 10.0000000000
b() == 10.0000000000
Distribution for 10 samples:
          1: -24.6503929840
          2: -16.3695641736
          3:   9.2130211326
          4:   9.3903679074
          5:  10.5893873999
          6:  10.5895397637
          7:  11.0045920062
          8:  20.9657242597
          9:  24.3894081218
         10:  35.2531547063

Requirements

Header: <random>

Namespace: std

See Also

Reference

<random>