Regularized incomplete beta function and real numbers

[markrogoyski]

Regularized incomplete beta function and real numbers

[Beakerboy]

The function is defined for a real numbers, but this algorithm only works for integer multiples of .5.

Implementing regularized incomplete beta for the rest will require a continuous fraction. I'll do it today.

[Beakerboy]

This is also in the pending pull request.

[markrogoyski]

Thanks for updating the function.

I added many unit tests and it looks good for most calculations. However, I found a case where the calculations don't match the online calculator I was using to create the unit test data.
When $a is a half integer (#.5) and $b is an integer, the result doesn't seem to match the online calculators.
For example:
$x = 0.55, $a = 2.5, $b = 2
This online calculator gives this result: 0.47672251 (http://www.analyticscalculators.com/calculator.aspx?id=37)

However, our function gives this result: 0.35452425122782244

Can you check this case?
Thanks.

[Beakerboy]

Will do. I was using the Mathworld Site for checking values.

[Beakerboy]

Those recursive functions in the top 'exact' part of the method are likely extensions of the translation functions in the bottom. I bet if I pull out my algebra skill, I can double check the for loop to make sure it's correct.

[Beakerboy]

I added a pull request to fix this.

[markrogoyski]

Merged pull request and added new unit tests. All tests pass.