# How does Matematica compute the CDF of the binomial distribution?

I want to know, how Mathematica actually implements the cumulative distribution function of the binomial distribution. Which algorithm does Mathematica use to compute CDF[BinomialDistribution[n, p], x]? Does Mathematica use the normal approximation, or does it use a better approximation?

So far I have found the sites about BinomialDistribution and CDF but I haven't found an answer to my question there. I know that Mathematica is closed source but is there a way get information about the actual used algorithm?

Note: I never have used Mathematica before.

• It evaluates the regularized incomplete beta function, which is built-in as BetaRegularized[], for appropriate arguments. As to what algorithm is being used to evaluate that… the docs only note that it uses hypergeometric function representations and continued fractions under the hood, and nothing more. – J. M.'s torpor Jul 21 '15 at 15:07
• You can see the use of BetaRegularized just by evaluating CDF[BinomialDistribution[n, p], x] – Bob Hanlon Nov 16 '15 at 19:23

It evaluates the regularized incomplete beta function, which is built-in as BetaRegularized[], for appropriate arguments. As to what algorithm is being used to evaluate that… the docs only note that it uses hypergeometric function representations and continued fractions under the hood, and nothing more.