cauchy_distribution Class
Generates a Cauchy distribution.
Syntax
template<class RealType = double>
class cauchy_distribution {
public:
// types
typedef RealType result_type;
struct param_type;
// constructor and reset functions
explicit cauchy_distribution(result_type a = 0.0, result_type 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
result_type a() const;
result_type 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>.
URNG
The uniform random number generator engine. For possible types, see <random>.
Remarks
The class template describes a distribution that produces values of a user-specified floating-point 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
param_type
The property functions a() and b() return their respective values for stored distribution parameters a and b.
The property member param() sets or returns the param_type stored distribution parameter package.
The min() and max() member functions return the smallest possible result and largest possible result, respectively.
The reset() member function discards any cached values, so that the result of the next call to operator() does not depend on any values obtained from the engine before the call.
The operator() member functions return the next generated value based on the URNG engine, either from the current parameter package, or the specified parameter package.
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);
}
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(result_type a = 0.0, result_type b = 1.0);
explicit cauchy_distribution(const param_type& parm);
Parameters
a
The a distribution parameter.
b
The b distribution parameter.
parm
The param_type 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<result_type> distribution_type;
param_type(result_type a = 0.0, result_type b = 1.0);
result_type a() const;
result_type b() const;
bool operator==(const param_type& right) const;
bool operator!=(const param_type& right) const;
};
Parameters
a
The a distribution parameter.
b
The b distribution parameter.
right
The param_type object to compare to this.
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.