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Evaluates the Bradford distribution PDF.

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Interface

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

using namespace Statistics::Distributions::Continuous::Bradford;

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

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

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

(1)

and

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

(2)

where

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

(3)

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. \graph a=0 b=0.7 c=2.5 x=0:0.8

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

Parameters

the argument of the PDF

the first parameter of the distribution (strictly less than b)

the second parameter of the distribution

the third parameter of the distribution (strictly positive)

Returns

the PDF of the Bradford 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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