PDF

Evaluates the Bradford distribution PDF.

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Interface
PDF
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Interface

C++

PDF

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

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

$P(x; a, b, c) = \frac{c}{(c(x - a) + b - a) \ln (c + 1)} \qquad \mbox{for } a < x \leq b$

(2)

and

$P(x; a, b, c) = 0 \qquad \mbox{for } x \leq a \quad \mbox{or} \quad x > b$

(3)

where

$a < b \quad and \quad c > 0$

(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, while the parameters have fixed values 0, 0.7 and 2.5 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 b=0.7 c=2.5 x=0:0.8

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

Example 1

#include <codecogs/statistics/distributions/continuous/bradford/pdf.h>
#include <iostream>
#include <iomanip>
 
#define PRECISION 17
 
int main()
{
  std::cout << "The values of the Bradford PDF with " << std::endl;
  std::cout << "a = 0, b = 0.7, c = 2.5 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::Bradford::PDF(x, 0, 0.7, 2.5);
    std::cout << std::endl;
  }
  return 0;
}

Output

The values of the Bradford PDF with
a = 0, b = 0.7, c = 2.5 and
x = {0, 0.1, 0.2, ... , 0.8} are
 
x =   0 : 0
x = 0.1 : 2.1006200003892843
x = 0.2 : 1.6629908336415169
x = 0.3 : 1.3762682761171172
x = 0.4 : 1.1738758825704825
x = 0.5 : 1.0233789745486259
x = 0.6 : 0.90708590925900912
x = 0.7 : 0.81452612259992652
x = 0.8 : 0

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 (strictly less than b)
b	the second parameter of the distribution
c	the third parameter of the distribution (strictly positive)

Returns

the PDF of the Bradford distribution

Authors

Lucian Bentea (September 2005)

Source Code

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