PDF

Evaluates the Anglit distribution PDF.

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Interface
PDF
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Interface

C++

Excel

PDF

doublePDF( double x )[inline]

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

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

(2)

The mean and variance of this distribution are given by

$\mu = 0$

(3)

and

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

(4)

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.

There is an error with your graph parameters for PDF with options x=-1:1

Error Message:Function PDF failed. Ensure that: Invalid C++

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

References

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

Parameters

x	the argument of the PDF

Returns

the PDF of the Anglit distribution

Authors

Lucian Bentea (September 2005)

Source Code

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double	`PDF` (double x)[inline] Evaluates the Anglit distribution PDF.
double	`mean`