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PDF

Evaluates the Burr distribution PDF.
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Interface

C++
HTML

PDF

 
doublePDFdoublex
doublea
doubleb
doublec
doubled )[inline]
This function evaluates the PDF of the Burr distribution with given arguments, defined by

where

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

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

References

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

Parameters

xthe argument of the PDF
athe first parameter of the distribution (less than or equal to x)
bthe second parameter of the distribution (strictly positive)
cthe third parameter of the distribution (strictly positive)
dthe 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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