gamma_distribution Class

Generates a gamma distribution.

Syntax

template<class RealType = double>
class gamma_distribution {
public:
    // types
    typedef RealType result_type;
    struct param_type;

    // constructors and reset functions
    explicit gamma_distribution(result_type alpha = 1.0, result_type beta = 1.0);
    explicit gamma_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 alpha() const;
    result_type beta() 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 template class describes a distribution that produces values of a user-specified floating-point type, or type double if none is provided, distributed according to the Gamma Distribution. The following table links to articles about individual members.

gamma_distribution gamma_distribution::alpha gamma_distribution::param
gamma_distribution::operator() gamma_distribution::beta param_type

The property functions alpha() and beta() return their respective values for stored distribution parameters alpha and beta.

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 gamma distribution, see the Wolfram MathWorld article Gamma 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::gamma_distribution<> distr(a, b);

    std::cout << std::endl;
    std::cout << "min() == " << distr.min() << std::endl;
    std::cout << "max() == " << distr.max() << std::endl;
    std::cout << "alpha() == " << std::fixed << std::setw(11) << std::setprecision(10) << distr.alpha() << std::endl;
    std::cout << "beta() == " << std::fixed << std::setw(11) << std::setprecision(10) << distr.beta() << 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 'alpha' distribution parameter (must be greater than zero): ";
    std::cin >> a_dist;
    std::cout << "Enter a floating point value for the 'beta' 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);
}
Use CTRL-Z to bypass data entry and run using default values.
Enter a floating point value for the 'alpha' distribution parameter (must be greater than zero): 1
Enter a floating point value for the 'beta' distribution parameter (must be greater than zero): 1
Enter an integer value for the sample count: 10

min() == 4.94066e-324
max() == 1.79769e+308
alpha() == 1.0000000000
beta() == 1.0000000000
Distribution for 10 samples:
    1: 0.0936880533
    2: 0.1225944894
    3: 0.6443593183
    4: 0.6551171649
    5: 0.7313457551
    6: 0.7313557977
    7: 0.7590097389
    8: 1.4466885214
    9: 1.6434088411
    10: 2.1201210996

Requirements

Header: <random>

Namespace: std

gamma_distribution::gamma_distribution

Constructs the distribution.

explicit gamma_distribution(result_type alpha = 1.0, result_type beta = 1.0);
explicit gamma_distribution(const param_type& parm);

Parameters

alpha
The alpha distribution parameter.

beta
The beta distribution parameter.

parm
The parameter structure used to construct the distribution.

Remarks

Precondition: 0.0 < alpha and 0.0 < beta

The first constructor constructs an object whose stored alpha value holds the value alpha and whose stored beta value holds the value beta.

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.

gamma_distribution::param_type

Stores the parameters of the distribution.

struct param_type {
   typedef gamma_distribution<result_type> distribution_type;
   param_type(result_type alpha = 1.0, result_type beta 1.0);
   result_type alpha() const;
   result_type beta() const;

   bool operator==(const param_type& right) const;
   bool operator!=(const param_type& right) const;
   };

Parameters

alpha
The alpha distribution parameter.

beta
The beta distribution parameter.

right
The param_type instance to compare this to.

Remarks

Precondition: 0.0 < alpha and 0.0 < beta

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>