normal_distribution Class

Generates a normal distribution.

Syntax

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

   // constructors and reset functions
   explicit normal_distribution(result_type mean = 0.0, result_type stddev = 1.0);
   explicit normal_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 mean() const;
   result_type stddev() 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 Normal Distribution. The following table links to articles about individual members.

normal_distribution normal_distribution::mean normal_distribution::param
normal_distribution::operator() normal_distribution::stddev param_type

The property functions mean() and stddev() return the values for the stored distribution parameters mean and stddev respectively.

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 Normal distribution, see the Wolfram MathWorld article Normal Distribution.

Example

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

using namespace std;

void test(const double m, const double s, const int samples) {

    // uncomment to use a non-deterministic seed
    //    random_device gen;
    //    mt19937 gen(rd());
    mt19937 gen(1701);

    normal_distribution<> distr(m, s);

    cout << endl;
    cout << "min() == " << distr.min() << endl;
    cout << "max() == " << distr.max() << endl;
    cout << "m() == " << fixed << setw(11) << setprecision(10) << distr.mean() << endl;
    cout << "s() == " << fixed << setw(11) << setprecision(10) << distr.stddev() << endl;

    // generate the distribution as a histogram
    map<double, int> histogram;
    for (int i = 0; i < samples; ++i) {
        ++histogram[distr(gen)];
    }

    // print results
    cout << "Distribution for " << samples << " samples:" << endl;
    int counter = 0;
    for (const auto& elem : histogram) {
        cout << fixed << setw(11) << ++counter << ": "
            << setw(14) << setprecision(10) << elem.first << endl;
    }
    cout << endl;
}

int main()
{
    double m_dist = 1;
    double s_dist = 1;
    int samples = 10;

    cout << "Use CTRL-Z to bypass data entry and run using default values." << endl;
    cout << "Enter a floating point value for the 'mean' distribution parameter: ";
    cin >> m_dist;
    cout << "Enter a floating point value for the 'stddev' distribution parameter (must be greater than zero): ";
    cin >> s_dist;
    cout << "Enter an integer value for the sample count: ";
    cin >> samples;

    test(m_dist, s_dist, samples);
}
Use CTRL-Z to bypass data entry and run using default values.
Enter a floating point value for the 'mean' distribution parameter: 0
Enter a floating point value for the 'stddev' 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
m() == 0.0000000000
s() == 1.0000000000
Distribution for 10 samples:
    1: -0.8845823965
    2: -0.1995761116
    3: -0.1162665130
    4: -0.0685154932
    5: 0.0403741461
    6: 0.1591327792
    7: 1.0414389924
    8: 1.5876269426
    9: 1.6362637713
    10: 2.7821317338

Requirements

Header: <random>

Namespace: std

normal_distribution::normal_distribution

Constructs the distribution.

explicit normal_distribution(result_type mean = 0.0, result_type stddev = 1.0);
explicit normal_distribution(const param_type& parm);

Parameters

mean
The mean distribution parameter.

stddev
The stddev distribution parameter.

parm
The parameter structure used to construct the distribution.

Remarks

Precondition: 0.0 < stddev

The first constructor constructs an object whose stored mean value holds the value mean and whose stored stddev value holds the value stddev.

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.

normal_distribution::param_type

Stores the parameters of the distribution.

struct param_type {
   typedef normal_distribution<result_type> distribution_type;
   param_type(result_type mean = 0.0, result_type stddev = 1.0);
   result_type mean() const;
   result_type stddev() const;

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

Parameters

mean
The mean distribution parameter.

stddev
The stddev distribution parameter.

right
The param_type structure used to compare.

Remarks

Precondition: 0.0 < stddev

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>