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Evaluates the variance of the Bradford distribution PDF.

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Interface

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

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

inline double variance(double a, double b, double c)

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

$\sigma^2(a, b, c) = (b - a)^2 \, \frac{c (L - 2) + 2L}{2cL^2} \qquad a < b \quad \mbox{and} \quad c > 0$

(1)

where

$L = \ln(c + 1)$

(2)

In the example that follows, the variance is evaluated using values of the third parameter from 0.1 up to 0.8 with a step equal to 0.1, while the other two parameters have fixed values, 0 and 1. The maximum number of precision digits, implicitly set to 17, may be changed through the <em> PRECISION </em> define.

Example 1

#include <codecogs/statistics/distributions/continuous/bradford/variance.h>
#include <iostream>
#include <iomanip>

#define PRECISION 17

int main()
{
  std::cout << "The variance of the Bradford distribution PDF with";
  std::cout << std::endl << "a = 0, b = 1 and " << std::endl;
  std::cout << "c = {0.1, 0.2, ... , 0.7, 0.8} is" << std::endl;
  std::cout << std::endl;
  for (double c = 0.1; c < 0.81; c += 0.1)
  {
    std::cout << std::setprecision(1);
    std::cout << "c = " << std::setw(3) << c << " : ";
    std::cout << std::setprecision(PRECISION);
    std::cout << Stats::Dists::Continuous::Bradford::variance(0.0, 1.0, c);
    std::cout << std::endl;
  }
  return 0;
}

Output

The variance of the Bradford distribution PDF with
a = 0, b = 1 and
c = {0.1, 0.2, ... , 0.7, 0.8} is

c = 0.1 : 0.083320719352760711
c = 0.2 : 0.083287201579144057
c = 0.3 : 0.0832378855758278
c = 0.4 : 0.083176514926087283
c = 0.5 : 0.083105887411104279
c = 0.6 : 0.083028127878180272
c = 0.7 : 0.082944872326977309
c = 0.8 : 0.082857395191116151

Parameters

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 variance of the Bradford distribution PDF

References

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

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