What is random header in C++ | Set 3 (Distributions)?

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random header in C++ | Set 3 (Distributions)️‍🔥

Set 1

Set 2

IV.Rate-based Distributions:

poisson_distribution	Poisson Distribution
exponential_distribution	Exponential Distribution
gamma_distribution	Gamma Distribution
weibull_distribution	Weibull Distribution
extreme_value_distribution	Extreme Value Distribution

1. poisson_distribution:

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 given by operator(), which in this case is always zero.

max: It returns the least upper bound of the range of values given by operator().

reset: It resets the distribution, so that subsequent uses of the object do not depend on values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of operator() in  
// poisson_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); 
  
  poisson_distribution<int> distribution (7.1); 
  
  cout << "Poisson-distribution(mean=5.0): "; 
  for (int i=0; i<10; ++i) 
    
    // use of operator() 
    cout << distribution(generator) << " "; 
  
  cout << endl; 
  
  return 0; 
}

Poisson-distribution(mean=5.0): 11 5 5 9 10 6 15 3 6 5

2. exponential_distribution

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operator():It generates the random number that are distributed according to the probability function.

max: It returns the least upper bound of the range of given by operator().

max:It returns the greatest lower bound of the range given by operator(), which is always zero for exponential_distribution.

reset:It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of  operator() in  
// exponential_distribution  
#include <iostream> 
#include <chrono> 
#include <thread> 
#include <random> 
using namespace std; 
  
// Driver program 
int main() 
{ 
  // It constructs 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); 
  
  exponential_distribution<double> distribution (1.0); 
    
  cout << "Hi's separated by 2 seconds, on average: \n"; 
  for (int i=0; i<5; ++i)  
  {       
    // use of operator() 
    double number = distribution(generator); 
    chrono::duration<double> period (number); 
      
    // It makes the thread sleep  
    // for the time period(i.e. number) 
    this_thread::sleep_for( period ); 
    cout << "Hi,Beginner!!" << endl; 
  } 
  
  return 0; 
}

Hi's separated by 2 seconds, on average: 
Hi,Beginner!!
Hi,Beginner!!

3. gamma_distribution

operator():It returns a new random number that follows the distribution’s parameters.

min:It returns the greatest lower bound of the range given by member operator(), which is always zero for gamma_distribution.

max:It returns the least upper bound of the range given by operator().

reset:It resets the distribution, so that on the subsequent uses the result does not depend on values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of reset in gamma_distribution 
#include <iostream> 
#include <random> 
using namespace std; 
   
// Driver program 
int main() 
{      
  // Random number generator 
  default_random_engine generator; 
  gamma_distribution<double> distribution(1.0,2.0); 
   
  // prints first random number 
  cout << distribution(generator) << endl; 
     
  // use of reset  
  distribution.reset(); 
     
  // prints the second random number  
  // independent of first 
  cout << distribution(generator) << endl; 
   
  return 0; 
}

1.14392
2.23359

4. weibull_distribution

operator():It returns a new random number that follows the distribution’s parameters.

min:It returns the greatest lower bound of the range given by operator(), which is always zero for weibull_distribution.

max:It returns the least upper bound of the range given by operator().

reset:It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of min and max 
// in weibull_distribution 
#include <iostream> 
#include <chrono> 
#include <random> 
using namespace std; 
  
// Driver program 
int main () 
{    
  // It constructs 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); 
  
  weibull_distribution<double> distribution (2.0,1.0); 
  
  cout << distribution(generator)  
       << " is a random number between "; 
    
  // use of min and max 
  cout << generator.min() << " and " << generator.max(); 
    
  return 0; 
} 

1.54229 is a random number between 1 and 2147483646

5. extreme_value_distribution

operator():It generates the random number that are distributed according to the probability function.

min:It returns the greatest lower bound of the range given by member operator().

max:It returns the least upper bound of the range given by member operator().

reset:It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of param in  
// extreme_value_distribution 
#include <iostream> 
#include <random> 
using namespace std; 
  
// Driver program 
int main() 
{ 
  default_random_engine generator; 
  extreme_value_distribution<double> d1(2.0,4.0); 
  extreme_value_distribution<double> d2(d1.param()); 
  
  // prints the first value 
  cout << d1(generator) << endl; 
    
  // prints the second independent value  
  cout << d2(generator) << endl; 
  
  return 0; 
} 

9.8351
3.95306

V. Related to Normal distribution

normal_distribution	Normal Distribution
lognormal_distribution	Lognormal Distribution
chi_squared_distribution	Chi-squared Distribution
cauchy_distribution	Cauchy Distribution
fisher_f_distribution	Fisher F-Distribution
student_t_distribution	Student T-Distribution

1. normal_distribution

where:
 (µ) :mean 
 sigma :standard deviation

operator():It generates the random number that are distributed according to the probability function.

min:It returns the greatest lower bound of the range given by operator().

max:It returns the least upper bound of the range given by operator().

reset:It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of operator() 
// in normal_distribution  
#include <iostream> 
#include <chrono> 
#include <random> 
using namespace std; 
  
// Driver program 
int main() 
{ 
  // It constructs 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); 
  
  // Initializes the normal distribution 
  normal_distribution<double> distribution (1.0,2.0); 
  
  cout << "Normal-distribution(1.0,2.0):" << endl; 
  for (int i=0; i<5; i++)   
    // Use of  operator() 
    cout << distribution(generator) << endl; 
  
  return 0; 
}

Normal-distribution(1.0,2.0):
1.59499
-0.458303
1.34411
0.138838
3.03433

2. lognormal_distribution

operator():It generates a random number which follows this distribution.

min:It returns the greatest lower bound of the range given by operator(), which is always zero for lognormal_distribution.

max:It returns the least upper bound of the range given by operator().

reset:It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of reset in  
// lognormal_distribution 
#include <iostream> 
#include <random> 
using namespace std; 
  
// Driver program 
int main() 
{ 
  // the random number generator 
  default_random_engine generator; 
  lognormal_distribution<double> distribution(1.0,2.0); 
  
  // prints first value: 
  cout << distribution(generator) << endl; 
    
  // Use of reset 
  distribution.reset(); 
    
  // prints second value independent of first 
  cout << distribution(generator) << endl; 
  
  return 0; 
} 

2.12989
10.6822

3. chi_squared_distribution

where,
n : degrees of freedom and n>0,
n/2 : shape parameter

operator():It generates the random number that are distributed according to the probability function.

min:It returns the greatest lower bound of the range given by operator(), which is always zero for the chi_squared_distribution.

max:It returns the least upper bound of the range given by operator().

reset:It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of operator() in  
// chi_squared_distribution  
#include <iostream> 
#include <chrono> 
#include <random> 
using namespace std; 
  
// Driver program 
int main() 
{ 
  // It constructs 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); 
  
  chi_squared_distribution<double> distribution (4.0); 
  
  cout << "chi-squared-distribution(4.0):" << endl; 
  for (int i=0; i<5; i++) 
      
    // use of operator() 
    cout << distribution(generator) << endl; 
  
  return 0; 
}

chi-squared-distribution(4.0):
2.18701
6.86953
1.77983
9.79626
5.04758

4. cauchy_distribution

where,
a and b are distribution parameters

operator():It generates the random number that are distributed according to the probability function.

min:It returns the greatest lower bound of the range given by operator().

max:It returns the least upper bound of the range given by operator().

reset: It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of param 
// in cauchy_distribution 
#include <iostream> 
#include <random> 
using namespace std; 
  
// Driver program 
int main() 
{ 
  default_random_engine generator; 
  cauchy_distribution<double> d1(0.0,1.0); 
  cauchy_distribution<double> d2(d1.param()); 
  
  // prints the first value 
  cout << d1(generator) << endl; 
    
  // prints the second value 
  cout << d2(generator) << endl; 
  
  return 0; 
} 

0.438486
7.65462

5. fisher_f_distribution

operator():It generates the random number that are distributed according to the probability function.

min:It returns the greatest lower bound of the range given by operator(), which is always zero for the fisher_f_distribution.

max:It returns the least upper bound of the range given by operator().

reset: It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of  
// operator() in fisher_f_distribution  
#include <iostream> 
#include <chrono> 
#include <random> 
using namespace std; 
  
// Driver program 
int main() 
{ 
  // It constructs 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); 
  
  fisher_f_distribution<double> distribution (1.0,2.0); 
  
  cout << "fisher-f-distribution(1.0,2.0):" << endl; 
  for (int i=0; i<5; i++) 
      
    // use of operator() 
    cout << distribution(generator) << endl; 
  
  return 0; 
} 

fisher-f-distribution(1.0,2.0):
0.208066
2.76882
0.0305701
0.96243
0.444256

6. student_t_distribution

where,
n is the distribution parameter

operator():It generates the random number that are distributed according to the probability function.

min:It returns the greatest lower bound of the range given by operator().

max:It returns the least upper bound of the range given by operator().

reset: It resets the distribution, so that on the subsequent uses the result does not depends on the values already produced by it.

param: It gets or sets the distribution parameter object .

// Illustrating the use of min and max 
// in student_t_distribution 
#include <iostream> 
#include <chrono> 
#include <random> 
using namespace std; 
   
// Driver program 
int main () 
{      
  // It constructs 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); 
   
  student_t_distribution<double> distribution (8.0); 
   
  cout << distribution(generator)  
       << " is a random number between "; 
     
  // use of min and max 
  cout << generator.min() << " and " << generator.max(); 
     
  return 0; 
} 

0.00906058 is a random number between 1 and 2147483646