In Probability, Discrete Uniform Distribution Function refers to the distribution with constant probability for discrete values over a range and zero probability outside the range. The probability density function P(x) for uniform discrete distribution in interval [a, b] is constant for discrete values in the range [a, b] and zero otherwise. Mathematically the function is defined as:
C++ have introduced uniform_int_distribution class in the random library whose member function give random integer numbers or discrete values from a given input range with uniform probabilty.
Public member functions in uniform_int_distribution class:
- operator(): This function returns a random number from the given range of distribution. The probability for any number to be obtained from this function is same. Operator() function takes constant time for generation.
Example:
// C++ code to demonstrate the working of
// operator() function
#include <iostream>
// for uniform_int_distribution function
#include <random>
using
namespace
std;
int
main()
{
// Here default_random_engine object
// is used as source of randomness
// We can give seed also to default_random_engine
// if psuedorandom numbers are required
default_random_engine generator;
int
a = 0, b = 9;
// Initializing of uniform_int_distribution class
uniform_int_distribution<
int
> distribution(a, b);
// number of experiments
const
int
num_of_exp = 10000;
int
n = b - a + 1;
int
p[n] = {};
for
(
int
i = 0; i < num_of_exp; ++i) {
// using operator() function
// to give random values
int
number = distribution(generator);
++p[number];
}
cout <<
"Expected probability: "
<<
float
(1) /
float
(n) << endl;
cout <<
"uniform_int_distribution ("
<< a <<
", "
<< b <<
")"
<< endl;
// Displaying the probability of each number
// after generating values 10000 times.
for
(
int
i = 0; i < n; ++i)
cout << a + i <<
": "
<< (
float
)p[i] / (
float
)(num_of_exp)
<< endl;
return
0;
}
chevron_rightfilter_noneOutput:Expected probability: 0.1 uniform_int_distribution (0, 9) 0: 0.0993 1: 0.1007 2: 0.0998 3: 0.0958 4: 0.1001 5: 0.1049 6: 0.0989 7: 0.0963 8: 0.1026 9: 0.1016
We could observe from the output that the probability of each number obtained from the random number is much closer to calculated probability.
- a(): Returns the lower parameter of range. This specifies the lower bound of the range of values potentially returned by its member operator().
- b(): Returns the higher parameter of range. This specifies the upper bound of the range of values potentially returned by its member operator().
- max(): This function return the possible smallest upper bound of output possible from the operator() function.
- min(): This function return the possible highest lower bound of output possible from the operator() function.
- reset(): This function resets the distribution such that subsequent distributions are not dependent on the previously generated numbers.
Example:
// C++ code to demonstrate the working of // a(), b(), min(), max(), reset() function #include <iostream> // for uniform_int_distribution function #include <random> using namespace std; int main() { int a = 10, b = 100; // Initializing of uniform_int_distribution class uniform_int_distribution< int > distribution(a, b); // Using a() and b() cout << "Lower Bound" << " " << distribution.a() << endl; cout << "Upper Bound" << " " << distribution.b() << endl; // Using min() and max() cout << "Minimum possible output" << " " << distribution.min() << endl; cout << "Maximum possible output" << " " << distribution.max() << endl; // Using reset() distribution.reset(); return 0; } |
Lower Bound 10 Upper Bound 100 Minimum possible output 10 Maximum possible output 100
Reference: https://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution
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