[Date Index]
[Thread Index]
[Author Index]
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,
Academic Press, 1990.
Dave Wagner
Principia Consulting
(303) 786-8371
dbwagner at princon.com
http://www.princon.com/princon
Prev by Date:
**Re: In[1]:= Question**
Next by Date:
**Re: play to wav?**
Previous by thread:
**Re: Random[BinomialDistribution[..]] wrong ?**
Next by thread:
**Re: Random[BinomialDistribution[..]] wrong ?**
| |