PDF

Evaluates the Burr distribution PDF.

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Interface
PDF
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Interface

C++

PDF

doublePDF(	double	`x`
	double	`a`
	double	`b`
	double	`c`
	double	`d`	)[inline]

This function evaluates the PDF of the Burr distribution with given arguments, defined by

$P(x; a, b, c, d) = \frac{cd}{b} \cdot \frac{1}{y^{c + 1}} \cdot \frac{1}{\left( 1 + y^{-c} \right)^{d + 1}} \qquad y = \frac{x - a}{b} \qquad \mbox{for } x \geq a$

(2)

where

$b > 0 \quad \mbox{and} \quad c > 0$

(3)

In the example that follows the PDF is evaluated using values of the argument from 0 up to 0.8, with a step equal to 0.1, while the parameters have fixed values -0.5, 0.7, 2.5 and 3.5 correspondingly. 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 a=-0.5:-0.1:4 b=0.7 c=2.5 d=3.5 x=0:1.5

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

Example 1

#include <codecogs/stats/dists/continuous/burr/pdf.h>
#include <iostream>
#include <iomanip>
 
#define PRECISION 17
 
int main()
{
  std::cout << "The values of the Burr PDF with " << std::endl;
  std::cout << "a = -0.5, b = 0.7, c = 2.5, d = 3.5 and" << std::endl;
  std::cout << "x = {0, 0.1, 0.2, ... , 0.8} are" << std::endl;
  std::cout << std::endl;
  std::cout << std::setprecision(10);
  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::Burr::PDF(x, -0.5, 0.7, 2.5, 3.5);
    std::cout << std::endl;
  }
  return 0;
}

Output

The values of the Burr PDF with
a = -0.5, b = 0.7, c = 2.5, d = 3.5 and
x = {0, 0.1, 0.2, ... , 0.8} are
 
x =   0 : 0.18355435441993792
x = 0.1 : 0.36639922215717169
x = 0.2 : 0.55242717280199027
x = 0.3 : 0.68930161452702099
x = 0.4 : 0.7573915683125797
x = 0.5 : 0.76439503593693336
x = 0.6 : 0.72910920987269623
x = 0.7 : 0.67006929817816285
x = 0.8 : 0.60112820540304646

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
a	the first parameter of the distribution (less than or equal to x)
b	the second parameter of the distribution (strictly positive)
c	the third parameter of the distribution (strictly positive)
d	the fourth parameter of the distribution

Returns

the PDF of the Burr distribution

Authors

Lucian Bentea (September 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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