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Evaluates the Bradford distribution CDF inverse.

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Interface

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

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

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

This function evaluates the CDF inverse of the Bradford distribution with given arguments, defined by

$D^{-1}(x, a, b, c) = a + \frac{b - a}{c} \left( (c + 1)^x - 1 \right) \qquad \mbox{for } 0 < x < 1$

(1)

and

$D^{-1}(x, a, b, c) = a \quad \mbox{for } x = 0 \qquad D^{-1}(x, a, b, c) = b \quad \mbox{for } x = 1$

(2)

where

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

(3)

In the example that follows, the CDF inverse is evaluated using values from 0 up to 0.8 with a step equal to 0.1. The maximum number of precision digits, implicitly set to 17, may be changed through the <em> PRECISION </em> define.

Example 1

#include <codecogs/stats/dists/continuous/bradford/cdf_inv.h>
#include <iostream>
#include <iomanip>

#define PRECISION 17

int main()
{
  std::cout << "The values of the Bradford CDF inverse with " << std::endl;
  std::cout << "a = 0, b = 0.7, c = 3 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::CDF_inv(x, 0, 0.7, 3);
    std::cout << std::endl;
  }
  return 0;
}

Output

The values of the Bradford CDF inverse with
a = 0, b = 0.7, c = 3 and
x = {0, 0.1, 0.2, ... , 0.8} are

x =   0 : 0
x = 0.1 : 0.03469628283264152
x = 0.2 : 0.074551845847008649
x = 0.3 : 0.12033386551909291
x = 0.4 : 0.17292359620485789
x = 0.5 : 0.23333333333333331
x = 0.6 : 0.30272589899861624
x = 0.7 : 0.38243702502735061
x = 0.8 : 0.47400106437151907

Parameters

the argument of the CDF inverse (in the interval from 0 to 1, including endpoints)

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 inverse CDF 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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