CodeCogs

Evaluates the Burr distribution PDF.

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Interface

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

using namespace Statistics::Distributions::Continuous::Burr;

inline double PDF(double x, double a, double b, double c, double d)

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

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

(1)

where

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

(2)

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. \graph a=-0.5:-0.1:4 b=0.7 c=2.5 d=3.5 x=0:1.5

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

Parameters

the argument of the PDF

the first parameter of the distribution (less than or equal to x)

the second parameter of the distribution (strictly positive)

the third parameter of the distribution (strictly positive)

the fourth parameter of the distribution

Returns

the PDF of the Burr 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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