random header | Set 2 (Distributions)

Difficulty Level : Easy
Last Updated : 29 May, 2017

Distributions

I. Uniform :

uniform_int_distribution: It produces random integer values i, which are uniformly distributed on the closed interval [a,b], which is described by the following probability mass function:

operator(): It generates the random number that are distributed according to the probability function.
min: It returns the greatest lower bound of the range of values returned by operator(), which is the distribution parameter ‘a’ for uniform_int_distribution.
max: It returns the least upper bound of the range of values returned by operator(), which is the distribution parameter ‘b’ for uniform_int_distribution.
reset: It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

// C++ program to illustrate
// the use of operator()
// in uniform_int_distribution
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
      
    // Constructing a trivial random generator engine 
    unsigned s = 2;
      
    // The random number generator
    default_random_engine generator (s);
      
    uniform_int_distribution<int> distribution(1,10);
    cout << "Some random numbers between 1 and 10";
    for (int i = 0; i < 10; ++i)
        cout << distribution(generator) ;
      
    cout << endl;
      
    return 0;
}

Output:

Some random numbers between 1 and 10: 1 3 6 10 1 5 1 4 4 9

// C++ program to illustrate
// the use of reset
// in uniform_int_distribution
#include <iostream>
#include <random>
using namespace std;
  
//Driver program
int main()
{
          
    //the random number generator
    default_random_engine generator;
      
    // Initialising the uniform distribution
    uniform_int_distribution<int> distribution(1, 1000);
      
    // First random number is generated
    cout << distribution(generator) << endl;
      
    //Resets the distribution
    distribution.reset();
      
    // Second random number is 
    //generated independent of previous number
    cout << distribution(generator) << endl;
      
    return 0;
}

Output:

1
132

uniform_real_distribution: It is the random number distribution that produces floating-point values , which is described by the following probability density function:

operator(): It returns a new random number that follows the distribution’s parameters.
min: It returns the greatest lower bound of the range of values returned by operator(), which is the distribution parameter ‘a’ for uniform_real_distribution.
max: It returns the least upper bound of the range of values returned by operator(), which is the distribution parameter ‘b’ for uniform_real_distribution.
reset: It resets the distribution, so that on the subsequent uses the result does not depend on values already produced by it.

// C++ program to illustrate
// the use of operator()
// in uniform_int_distribution
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
      
    // Constructing a trivial random generator engine 
    unsigned s = 2;
      
    // The random number generator
    default_random_engine generator (s);
      
    uniform_int_distribution<int> distribution(1,10);
    cout << "Random numbers between 1 and 10";
    for (int i = 0; i< 10; ++i)
        cout << distribution(generator) ;
      
    cout << endl;
      
    return 0;
}

Output:

some random numbers between 0.0 and 10.0: 
0.150031
9.77072
3.36669
7.06447
5.11455
8.43061
1.93792
7.78965
8.31532
5.14354

// C++ program to illustrate
// the use of reset
// in uniform_real_distribution
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
    default_random_engine generator;
    uniform_real_distribution<double> distribution(0.0,100.0);
      
    // It prints two independent values:
    // First random number is generated
    cout << distribution(generator) << endl;
      
    //Resets the distribution
    distribution.reset();
      
    // Second random number is 
    //generated independent of previous number
    cout << distribution(generator) << endl;
      
    return 0;
}

Output:

13.1538
45.865

II. Related to bernoulli trials:

bernoulli_distribution: It is the random number distribution that produces bool values according to a Bernoulli distribution, given by the following probability mass function:

operator(): It returns a new random number.
min: It returns the greatest lower bound of the range of values returned by operator(), which for bernoulli_distribution is false.
max: It returns the least upper bound of the range of values returned by operator(), which for bernoulli_distribution is true.

// C++ program to illustrate
// the bernoulli_distribution
#include <iostream>
#include <random>
using namespace std;
  
//Driver program
int main()
{
    const int temp=500;
      
    //The random number generator
    default_random_engine generator;
      
    //Initialising the bernoulli distribution
    bernoulli_distribution distribution(0.7);
      
    // count number of trues
    int count=0; 
      
    for (int i = 0; i < temp; ++i) 
    {
          
        // checking for true condition 
        if (distribution(generator)) 
        count++;
    }
      
    cout << "bernoulli_distribution (0.7) x 500:" << endl;
    cout << "true: " << count << endl;
    cout << "false: " << temp-count << endl;
      
    return 0;
}

Output:

bernoulli_distribution (0.7) x 500:
true:  360
false: 140

// C++ program to
// illustrate the use of reset
#include <iostream>
#include <random>
using namespace std;
  
//Driver program
int main()
{
    // Random number generator
    default_random_engine generator;
      
    // Initialising the bernoulli distribution
    bernoulli_distribution distribution;
      
    // print two independent values:
    cout << distribution(generator) << endl;
      
    // use of reset
    // Generates second output without
    // the effect of first output 
    distribution.reset();
    cout << distribution(generator) << endl;
  
return 0;
}

Output:

1
1

binomial_distribution: It is the random number distribution that produces integers according to a binomial discrete distribution, which is given by this probability mass function:

operator(): It generates a new random number.
max: It returns the least upper bound of the range given by operator(), which for binomial_distribution is the distribution parameter t.
min: It returns the greatest lower bound of the range given by member operator(), which for binomial_distribution is always zero.
reset: It resets the distribution, so that subsequent uses of the object do not depend on values already produced by it.

// C++ program to illustrate
// the use of binomial_distribution
#include <iostream>
#include <chrono>
#include <random>
using namespace std;
  
int main()
{
      
    // construct a trivial random 
    //generator engine from a time-based seed:
    unsigned seed = chrono::system_clock::now().time_since_epoch().count();
    default_random_engine generator (seed);
      
    // Initialising binomial distribution
    binomial_distribution<int> distribution (15, 0.4);
      
    cout << "some binomial results (t=15, p=0.4): ";
    for (int i = 0; i < 15; ++i)
    {
              
        // Use of operator()
        cout << distribution(generator) << " ";
    }
    cout << endl;
      
    return 0;
}

Output:

some binomial results (t=15, p=0.4): 7 6 7 8 4 6 7 6 9 3 5 6 4 6 7

// C++ program to illustrate
// the use of binomial_distribution
#include <iostream>
#include <chrono>
#include <random>
using namespace std;
  
int main()
{
      
    // construct a trivial random 
    //generator engine from a time-based seed:
    unsigned seed = chrono::system_clock::now().time_since_epoch().count();
    default_random_engine generator (seed);
      
    // Initialising binomial distribution
    binomial_distribution<int> distribution (15, 0.4);
      
    cout << "some binomial results (t=15, p=0.4): ";
    for (int i = 0; i < 15; ++i)
    {
              
        // Use of operator()
        cout << distribution(generator) << " ";
    }
    cout << endl;
      
    return 0;
}

Output:

57
52

geometric_distribution: It is a random number distribution that produces integers according to a geometric discrete distribution, given by the following probability mass function:

operator(): It returns a new random number that follows the distribution’s parameters.
max: It returns least upper bound of the range given by operator().
min: It returns the minimum value given by operator().
reset: It resets the distribution, so that subsequent uses of the object do not depend on values already produced by it.

// C++ program to illustrate
//the use of geometric_distribution 
#include <iostream>
#include <chrono>
#include <string>
#include <random>
using namespace std;
  
int main()
{
    // construct a trivial random
    // generator engine from a time-based seed:
    int seed = chrono::system_clock::now().time_since_epoch().count();
    default_random_engine generator (seed);
      
    // Initialises the geometric distribution
    geometric_distribution<int> distribution (1.0 / 5);
      
    cout << "Plus sign is 5 spaces away from the next :" << endl;
    for (int i = 0; i < 10 ; ++i) 
    {
        int number = distribution(generator);
        cout << string (number,' ') << "+";
    }
  
return 0;
}

Output:

each plus sign is 5 spaces away from the next :
            ++ + +   +  ++     +        ++

// C++ program to illustrate 
// the use of reset
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
      
    // Random number generator 
    default_random_engine generator;
      
    // Initialising the geometric distribution
    geometric_distribution<int> distribution(0.3);
      
    // Prints two independent values:
    // Generates the first value
    cout << distribution(generator) << endl;
      
    // Use of reset
    distribution.reset();
      
    // Generates second value
    cout << distribution(generator) << endl;
      
    return 0;
}

Output:

0
1

negative_binomial_distribution: It is a random number distribution that produces integers according to a negative binomial discrete distribution (also known as Pascal distribution), given by the following probability mass function:

operator():It returns a new random number which follows the distribution’s parameters.
max:It returns least upper bound of the range given by operator().
min:It returns the minimum value given by operator(),which for negative_binomial_distribution is always zero.
reset: It resets the distribution, so that subsequent uses of the object do not depend on values already produced by it.

// C++ program to illustrate
// the use of operator() in
// negative_binomial_distribution 
#include <iostream>
#include <chrono>
#include <random>
using namespace std;
  
// Driver program
int main()
{
    // construct a trivial random 
    // generator engine from a time-based seed:
    unsigned seed = chrono::system_clock::now().time_since_epoch().count();
    default_random_engine generator (seed);
      
    // Initialising negative binomial distribution
    negative_binomial_distribution<int> distribution (6,0.7);
      
    cout << "Negative binomial results (t=6, p=0.7): ";
    for (int i = 0; i < 15; ++i)
        {
            // Use of operator
            cout << distribution(generator) << " ";
        }
      
    cout << endl;
      
    return 0;
}

Output:

Negative binomial results (t=6, p=0.7): 2 6 3 1 4 1 4 1 2 0 7 3 4 4 4

// C++ program to illustrate
// the use of reset in
// negative_binomial_distribution::
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
      
    // Random number generator 
    default_random_engine generator;
      
    // Initialising the negative binomial distribution
    negative_binomial_distribution<int> distribution(20, 0.5);
      
    // print two independent values:
    // Generates the first value
    cout << distribution(generator) << endl;
      
    // Use of reset
    distribution.reset();
      
    // Generates the second value
    cout << distribution(generator) << endl;
      
    return 0;
}

Output:

23
30

III.Piece wise distributions:

discrete_distribution: It is a random number distribution that produces integer values according to a discrete distribution.

operator(): It returns a new random number that follows the distribution’s parameters.
max: It returns the least upper bound of the range given by operator().
min: It returns the greatest lower bound of the range given by operator().
reset: It resets the distribution, so that subsequent uses of the object do not depend on values already produced by it.

// C++ program to illustrate the
// use of operator() in
// discrete_distribution
#include <iostream>
#include <random>
using namespace std;
  
int main()
{
      
    // number of experiments
    int n = 10000; 
      
    // maximum number of stars to distribute
    int m = 100; 
      
    // Random number generator
    default_random_engine generator;
      
    //Initialising discrete distribution
    discrete_distribution<int> distribution { 2, 2, 1, 1, 2, 2, 1, 1, 2, 2 };
      
    int p[10] = {};
      
    // use of operator()
    for (int i = 0; i < n; i++) 
    {
        int number = distribution(generator);
        p[number]++;
    }
      
    cout << "a discrete_distribution:" << endl;
    for (int i = 0; i < 10; ++i)
    {
        cout << i << ": " << string(p[i]*m/n,'*') << endl;
    }
      
    return 0;
}

Output:

a discrete_distribution:
0: ************
1: *************
2: *****
3: ******
4: ************
5: ************
6: ******
7: ******
8: ************
9: ************

// C++ program to illustrate
//the use of reset in
//discrete_distribution
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
      
    // Random number generator 
    default_random_engine generator;
      
    // Initialising the discrete distribution
    discrete_distribution<int> distribution {20,20,30,40};
      
    // print two independent values:
    // Generates the first value
    cout << distribution(generator) << endl;
      
    // Use of reset
    distribution.reset();
      
    // Generates the secong value
    cout << distribution(generator) << endl;
      
    return 0;
}

Output:

0
2

piecewise_constant_distribution: It is a random number distribution that produces floating-point values that are uniformly distributed over each of a sequence of contiguous subintervals, given by following probability density function:

operator(): It returns a new random number that follows the distribution’s parameters.
max: It returns the least upper bound of the range given by operator().
min: It returns the greatest lower bound of the range given by operator().
reset: It resets the distribution, so that subsequent uses of the object do not depend on values already produced by it.

// C++ program to illustrate the
// use of reset in
// piecewise_constant_distribution
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
      
    // Random number generator
    default_random_engine generator;
      
    // Initialisind piecewise_constant_distribution
    piecewise_constant_distribution<double> distribution 
                ( 4, 0.0, 10.0, [](double x){return x;} );
      
    // print two independent values:
    // Generates the first value
    // Use of operator()
    cout << distribution(generator) << endl;
      
    // Use of reset
    distribution.reset();
      
    // Generates second value
    cout << distribution(generator) << endl;
      
    return 0;
}

Output:

3.4205
6.6692

piecewise_linear_distribution: It is a random number distribution that produces floating-point values that are distributed over a sequence of contiguous subintervals.

operator():It returns a new random number that follows the distribution’s parameters.
max: It returns the least upper bound of the range given by operator().
min: It returns the greatest lower bound of the range given by operator().
reset: It resets the distribution, so that subsequent uses of the object do not depend on values already produced by it.

// C++ program to illustrate the
// use of reset in
// piecewise_linear_distribution
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
      
    // Random number generator
    default_random_engine generator;
      
    // Initialising piecewise_linear_distribution
    piecewise_linear_distribution<double>
        distribution ( 5, 0.0, 10.0, [](double x){return x+1.0;} );
      
    // print two independent values:
    // generates first value
    // use of operator()
    cout << distribution(generator) << endl;
      
    // Use of reset
    distribution.reset();
      
    // generates second value
    cout << distribution(generator) << endl;
      
    return 0;
}

Output:

2.48143
6.07656

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