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# variance

Evaluates the variance of the Bradford distribution PDF.
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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

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

where

$L&space;=&space;\ln(c&space;+&space;1)$

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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Last Modified: 17 Apr 13 @ 18:15     Page Rendered: 2022-03-14 17:51:51