Re: binocdf inaccuracy in Octave

[Daniel J Sebald]

On 07/08/2013 11:38 AM, Rik wrote:
> 7/8/13
>
> Dr. Klein,
>
> I think this is actually a much easier problem to solve that it first
> appeared.  In the the file binocdf.m the formula used to calculate the
> CDF is
>
> cdf(k) = 1 - betainc (p, tmp + 1, n - tmp);
>
> According to Wikipedia
> (http://en.wikipedia.org/wiki/Binomial_distribution) the CDF for the
> binomial distribution is
>
> \textstyle I_{1-p}(n - k, 1 + k)
>
> or
>
> I(1-p, n-k, 1+k)
>
> So it appears that we simply have the arguments wrong to the betainc
> function.

But it is also true that

\textstyle I_{x}(a, b) = I_{1-x}(b, a)

http://en.wikipedia.org/wiki/Regularized_incomplete_beta_function#Incomplete_beta_function

In other words, the two expressions you are comparing are mathematically 
equivalent.  Where is the discrepancy then?  Numerical issues?

Dan