cauchy_distribution a() in C++ with Examples

The cauchy_distribution::a() function is an inbuilt function in C++ STL which is used to returns the distribution parameter associated with Cauchy distribution. The class cauchy_distribution is present in header file random. Before going to the syntax of the function, brief introduction to Cauchy Distribution.

Cauchy Distribution A random variable X is said to follow Cauchy Distribution with parameter a and b if it has the probability density function of the form,
 f(x)=\frac{1}{\pi b[1+(\frac{x-a}{b})^2]}

Where a is the location parameter specifying the location of peak of the distribution and b is the scale parameter specifying the half-width at half-maximum. Mean and Variance of the distribution is not defined, but its median and mode both exists and equals to a.

Syntax:

cauchy_distribution_name.a()

Parameters: This function does not accepts any parameter.

Return Value: The function returns the distribution parameter associated with the distribution. This parameter is known as the peak location parameter of the Cauchy distribution, which determines the shift to either side of the distribution shape. The parameter is set on construction.

Below programs illustrates the cauchy_distribution::a() function in C++ STL:

Program 1:

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// CPP program to illustrate
// cauchy_distribution::a()
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
    default_random_engine generator;
    cauchy_distribution<double> d(0.78, 1.45);
  
    // prints the first value
    cout << "Cauchy distribution: " << d.a();
  
    return 0;
}

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Output:

Cauchy distribution: 0.78

Program 2:

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// CPP program to illustrate
// cauchy_distribution::a()
#include <iostream>
#include <random>
using namespace std;
  
// Driver program
int main()
{
    default_random_engine generator;
  
    // Define a cauchy distribution with default 
    // parameters a=0.0 and b=1.0
    cauchy_distribution<double> d;
  
    // prints the first value
    cout << "Cauchy distribution: " << d.a();
  
    return 0;
}

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Output:

Cauchy distribution: 0


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