variance

Evaluates the variance of the Bradford distribution PDF.

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Interface
Variance
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Interface

C++

Variance

doublevariance(	double	`a`
	double	`b`
	double	`c`	)[inline]

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

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

(2)

where

$L = \ln(c + 1)$

(3)

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

References

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

Parameters

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 variance of the Bradford distribution PDF

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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