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

• Difficulty Level : Expert
• Last Updated : 12 Feb, 2018

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 #include #include using namespace std;  // Driver Programint 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 #include #include #include using namespace std;  // Driver programint 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 distributionâ€™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 #include using namespace std;   // Driver programint 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 distributionâ€™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 #include #include using namespace std;  // Driver programint 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 #include using namespace std;  // Driver programint 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:
(Âµ) :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 #include #include using namespace std;  // Driver programint 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 #include using namespace std;  // Driver programint 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 #include #include using namespace std;  // Driver programint 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 #include using namespace std;  // Driver programint 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 #include #include using namespace std;  // Driver programint 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 #include #include using namespace std;   // Driver programint 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

This article is contributed by Shambhavi Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes arrow_drop_up