random header | Set 2 (Distributions)

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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