From: "Alain Boulanger" Subject: Re: Negative Binomial Date: Sun, 31 Jan 1999 08:39:03 -0500 Newsgroups: sci.math Keywords: Negative binomial / hypergeometric distribution Arthur C Clay a écrit dans le message <790fmb$8uv@senator-bedfellow.MIT.EDU>... >I am looking for a formula which I believe >is labeled the "Negative Binomial". It is >supposed to handle the following type of >probability problem: what is the probability >of getting the nth item on the rth draw, given >that there are a total of N items, N' of which >are identical to n. An example would be finding >the probability of obtaining the 3rd spade on >the 6th draw, or thereabouts. > >Also, is this in any way related to the >hypergeometric distribution? > Yes indeed! look under negative hypergeometric! You have to look at the ways all N' could be sampled from the N object and ask in how many ways the n-th would appear on the r-th draw In general if you want the n-th of a kind (N' of that kind from N object) at the r-th draw (without replacement), you need: (n-1) on the first (r-1) draws: (r-1)! / [ (n-1)! (r-n)! ] 1 on the r-th draw: 1 (N'-n) would appear on the next (N-r) draws: ((N-r)! / [ (N'-n)! (N-r-N'+n)! ] So the probability would be: (r-1)! / [ (n-1)! (r-n)! ] * 1 * ((N-r)! / [ (N'-n)! (N-r-N'+n)! ] ---------------------------------------------------------------------------- N! / [ N'! (N-N')!] ============================================================================== From: phunt@interpac.net Subject: Re: Negative Binomial Date: Sun, 31 Jan 1999 15:26:54 GMT Newsgroups: sci.math In article <790fmb$8uv@senator-bedfellow.MIT.EDU>, acclay@mit.edu (Arthur C Clay) wrote: > the probability of obtaining the 3rd spade on > the 6th draw, or thereabouts. Use the negative binomial to find the probability of obtaining the 3rd spade on exactly the 6th draw. Use the hypergeometric to find the probability of obtaining 3 spades (without regard for order) after having drawn 6 cards. Both distributions are related to the binomial distribution, but whereas the binomial distribution replaces the random variable following each draw, the negative binomial and hypergeometric do not. The formulas are hard to write in ASCII ... You can find them. /ph - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - In article <790fmb$8uv@senator-bedfellow.MIT.EDU>, acclay@mit.edu (Arthur C Clay) wrote: [original article; deleted -- djr] -----------== Posted via Deja News, The Discussion Network ==---------- http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own