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

We have discussed generators in Set 1. We have also discussed three distributions in Set 2. In this post, more distributions are discussed. 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: It is a distribution that produces integers according to a Poisson distribution, which is given by the following probability mass 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 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;
}

Output:

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

2. exponential_distribution: It is a random number distribution that produces floating-point values according to an exponential distribution, given by:

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,Geeks!!" << endl;
  }

  return 0;
}

Output:

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

3. gamma_distribution: It is a random number distribution that produces floating-point values according to a gamma distribution, given by:

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;
}

Output:

1.14392
2.23359

4. weibull_distribution:It is a random number distribution that produces floating-point values according to a 2-parameter Weibull distribution,given by:

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;
}

Output:

1.54229 is a random number between 1 and 2147483646

5. extreme_value_distribution:It is a random number distribution that produces floating-point values according to a Type I extreme value distribution,given by:

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;
}

Output:

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: It is a random number distribution that produces floating-point values according to a normal distribution, given by:

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;
}

Output:

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

2. lognormal_distribution:It is a random number distribution that produces floating-point values according to a lognormal distribution, given by:

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;
}

Output:

2.12989
10.6822

3. chi_squared_distribution:It is a random number distribution that produces floating-point values according to a chi-squared distribution,given by:

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;
}

Output:

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

4. cauchy_distribution:It is a random number distribution that produces floating-point values according to a Cauchy distribution, given by:

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;
}

Output:

0.438486
7.65462

5. fisher_f_distribution:It is a random number distribution that produces floating-point values according to a Fisher F-distribution, given by: It produces random numbers by dividing two independent Chi-squared distributions of m and n degrees of freedom.

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;
}

Output:

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

6. student_t_distribution:It is a random number distribution that produces floating-point values according to a Student T-distribution, given by:

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;
}

Output:

0.00906058 is a random number between 1 and 2147483646