random header | Set 2 (Distributions)
Distributions
- 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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
23 30
-
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
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;
}
chevron_rightfilter_noneOutput:
2.48143 6.07656
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