CDF inv

Evaluates the Bradford distribution CDF inverse.

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Interface
CDF Inv
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Interface

C++

CDF Inv

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

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

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

(2)

and

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

(3)

where

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

(4)

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.

There is an error with your graph parameters for CDF_inv with options x=0:0.8 a=0 b=0.7 c=1:5:5

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

Example 1

#include <codecogs/statistics/distributions/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

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

Authors

Lucian Bentea (September 2005)

Source Code

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