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Re: binocdf inaccuracy in Octave


From: Daniel J Sebald
Subject: Re: binocdf inaccuracy in Octave
Date: Mon, 08 Jul 2013 12:33:08 -0500
User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv:1.9.2.24) Gecko/20111108 Fedora/3.1.16-1.fc14 Thunderbird/3.1.16

On 07/08/2013 12:29 PM, Daniel J Sebald wrote:
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)

Oops, make that

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

Dan

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


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