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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