CDF

Evaluates the Burr distribution CDF.

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Interface
CDF
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Interface

C++

CDF

doubleCDF(	double	`x`
	double	`a`
	double	`b`
	double	`c`
	double	`d`	)[inline]

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

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

(2)

and

$D(x, a, b, c, d) = 0 \quad \mbox{for } x \leq a$

(3)

where b and c have strictly positive values.

In the example that follows, the CDF is evaluated using values from 0 up to 2, while the parameters a,b,c,d have fixed values -0.5, 0.7, 2.5 and 3.5 respectively.

There is an error with your graph parameters for CDF with options x=0:2 a=-0.5 b=0.7 c=2.5 d=3.5

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

The maximum number of precision digits, implicitly set to 17, may be changed through the PRECISION define.

Example 1

#include <codecogs/statistics/distributions/continuous/burr/cdf.h>
#include <iostream>
#include <iomanip>
 
#define PRECISION 17
 
int main()
{
  std::cout << "The values of the Burr CDF 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::CDF(x, -0.5, 0.7, 2.5, 3.5);
    std::cout << std::endl;
  }
  return 0;
}

Output

The values of the Burr CDF 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 : 0.015011611611517064
x = 0.1 : 0.042214073569134036
x = 0.2 : 0.088388347648318433
x = 0.3 : 0.15101951651603249
x = 0.4 : 0.22392439421917074
x = 0.5 : 0.30045023519396202
x = 0.6 : 0.37539504317313416
x = 0.7 : 0.44548599437492181
x = 0.8 : 0.50908462139895982

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
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)
d	the fourth parameter of the distribution

Returns

the CDF 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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