• https://me.yahoo.com
COST (GBP)
0.20
0.00
0

# mean

Evaluates the mean of the Bradford distribution PDF.
Contents

C++
Excel

## Mean

 doublemean( double a double b double c )[inline]
This function evaluates the mean of the Bradford distribution PDF with given arguments, defined by

$\mu(a,&space;b,&space;c)&space;=&space;\frac{1}{cL}&space;(c(b&space;-&space;a)&space;+&space;L(a(c&space;+&space;1)&space;-&space;b))&space;\qquad&space;a&space;<&space;b&space;\quad&space;\mbox{and}&space;\quad&space;c&space;>&space;0$

where

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

In the example that follows, the mean 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/stats/dists/continuous/bradford/mean.h>
#include <iostream>
#include <iomanip>

#define PRECISION 17

int main()
{
std::cout << "The mean 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 << std::endl;
}
return 0;
}

### Output

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

c = 0.1 : 0.49205868725706231
c = 0.2 : 0.48481494774707845
c = 0.3 : 0.4781613533750686
c = 0.4 : 0.47201341198846192
c = 0.5 : 0.46630346237643167
c = 0.6 : 0.46097647856777624
c = 0.7 : 0.45598710746256077
c = 0.8 : 0.45129752801813683

### 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 mean 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.

Not a member, then Register with CodeCogs. Already a Member, then Login.