random header | Set 2 (Distributions)

Set 1 (Generators)

Distributions

I. Uniform :

1. 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
   

2. 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:

1. 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
   

2. 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
   

3. 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
   

4. 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:

1. 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
   

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
   

3. 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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