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 probability.
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-a];
}
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;
} |
Output:
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;
} |
Output:
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