       Re: Random[BinomialDistribution[..]] wrong ?

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1103] Re: Random[BinomialDistribution[..]] wrong ?
• From: wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner)
• Date: Sun, 14 May 1995 23:11:37 -0400
• Organization: University of Colorado, Boulder

```In article <3os8a8\$r7q at news0.cybernetics.net>,
David Withoff <withoff at wri.com> wrote:
>The most common way of dealing with this problem that I have seen
>is to approximate CDF[BinomialDistribution[n, p], k] for large
>values of n with something that is easier to calculate.  Those
>large-n formulas that you see in elementary statistics books are
>useful not only because they make it easier to find things in common
>tables, but because they are easier to evaluate numerically.  So
>my real recommendation, rather than crank up the precision for
>BetaRegularized, is to find a large-n approximation for quantiles
>of the binomial distribution.
>
>Dave Withoff
>Research and Development
>Wolfram Research

Well I just happen to have my large-n binomial approximation in my
pocket here...

Sum[Binomial[n,k], {k,a,b}] is approximately equal to:

Phi[(b - n p + 1/2)/Sqrt[n p q]] -
Phi[(a - n p - 1/2)/Sqrt[n p q]]

where Phi is the unit normal distribution function, of course, and
q = 1 - p.

Furthermore, if n is large and p is small, you can approximate the binomial
distribution with a Poisson(n*p) distribution.

Source: A.O. Allen, Probability, Statistics, and Queueing Theory,

Dave Wagner
Principia Consulting
(303) 786-8371
dbwagner at princon.com
http://www.princon.com/princon

```

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