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Evaluates the Anglit distribution PDF.

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Interface

#include <codecogs/statistics/distributions/continuous/anglit/pdf.h>

using namespace Statistics::Distributions::Continuous::Anglit;

inline double PDF(double x)

This function evaluates the PDF of the Anglit distribution with given argument, defined by

$P(x) = \sin \left( 2x + \frac{\pi}{2} \right) \qquad -\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$

(1)

The mean and variance of this distribution are given by

$\mu = 0$

(2)

and

$\sigma^2 = \int_{-\pi/4}^{\pi/4} x^2 \sin \left(2x + \frac{\pi}{2}\right) \mathrm{d}x = \frac{1}{16} \pi^2 - \frac{1}{2}$

(3)

In the example that follows, the PDF is evaluated using values from 0 up to 0.8 with a step equal to 0.1. The mean and variance of the distribution, stored as constants inside the same namespace, are also displayed. The maximum number of precision digits, implicitly set to 17, may be changed through the <em> PRECISION </em> define.

\graph x=-1:1

Example 1

#include <codecogs/stats/dists/continuous/anglit/pdf.h>
#include <iostream>
#include <iomanip>

#define PRECISION 17

int main()
{
  std::cout << "The values of the Anglit PDF with";
  std::cout << std::endl;
  std::cout << "x = {0, 0.1, 0.2, ... , 0.7, 0.8} are" << std::endl;
  std::cout << std::endl;
  for (double x = 0; x < 0.81; x += 0.1)
  {
    std::cout << std::setprecision(1);
    std::cout << "x = " << std::setw(3) << x << " : ";
    std::cout << std::setprecision(PRECISION);
    std::cout << Stats::Dists::Continuous::Anglit::PDF(x);
    std::cout << std::endl;
  }
  std::cout << std::endl;
  std::cout << "The mean of the Anglit distribution is";
  std::cout << std::endl;
  std::cout << Stats::Dists::Continuous::Anglit::mean;
  std::cout << std::endl;
  std::cout << "and variance is" << std::endl;
  std::cout << Stats::Dists::Continuous::Anglit::variance;
  std::cout << std::endl;
  return 0;
}

Output:

The values of the Anglit PDF with
x = {0, 0.1, 0.2, ... , 0.7, 0.8} are

x =   0 : 0.70710678118654746
x = 0.1 : 0.83349215422481648
x = 0.2 : 0.926648825310733
x = 0.3 : 0.98286293194097685
x = 0.4 : 0.99989339507807162
x = 0.5 : 0.97706126389947567
x = 0.6 : 0.91527678342432328
x = 0.7 : 0.8170031059169558
x = 0.8 : 0

The mean of the Anglit distribution is
0
and variance is
0.11685027506808487

Parameters

the argument of the PDF

Returns

the PDF of the Anglit distribution

References

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

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