cauchy_distribution Class

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

Generates a Cauchy distribution.

Syntax

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.

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

cauchy_distribution::cauchy_distribution

Constructs the distribution.

explicit cauchy_distribution(RealType a = 0.0, RealType b = 1.0);

 
explicit cauchy_distribution(const param_type& parm);

Parameters

a
The a distribution parameter.

b
The b distribution parameter.

parm
The parameter structure used to construct the distribution.

Remarks

Precondition: 0.0 < b

The first constructor constructs an object whose stored a value holds the value a and whose stored b value holds the value b.

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.

cauchy_distribution::param_type

Stores all the parameters of the distribution.

struct param_type {  
   typedef cauchy_distribution<RealType> distribution_type;  
   param_type(RealType a = 0.0, RealType b = 1.0);
   RealType a() const;
   RealType b() const;
   .....  
   bool operator==(const param_type& right) const;
   bool operator!=(const param_type& right) const;
   };  

Parameters

See parent topic cauchy_distribution Class.

Remarks

Precondition: 0.0 < b

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.

See Also

<random>