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Evaluates the Burr distribution CDF.

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Interface

#include <codecogs/statistics/distributions/continuous/burr/cdf.h>

using namespace Statistics::Distributions::Continuous::Burr;

inline double CDF(double x, double a, double b, double c, double d)

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

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

(1)

and

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

(2)

where b and c have strictly positive values.

In the example that follows, the CDF is evaluated using values from 0 up to 0.8, with a step equal to 0.1, while the parameters have fixed values -0.5, 0.7, 2.5 and 3.5 correspondingly. 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/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

Parameters

the argument of the CDF

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

the second parameter of the distribution

the third parameter of the distribution (strictly positive)

the fourth parameter of the distribution

Returns

the CDF of the Burr 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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Result –