Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2000
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

RE: mean of geometric and negative binomial distributions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24077] RE: [mg24066] mean of geometric and negative binomial distributions
  • From: Tomas.Garza at smc.vnet.net
  • Date: Fri, 23 Jun 2000 02:26:44 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

It is a matter of definition. Most sources define the geometric distribution as the waiting time for the occurrence of a binomial event, i.e., the number of trials up to and including the first "success". In this case the expected value is 1/p. However, Mathematica uses the definition "number of trials before the first success", and then the expected value is (1 - p)/p. Here the number of trials is one less than in the former case, and then the expected value is equal to 1/p - 1 = (1 - p)/p. A similar reasoning provides the answer for the negative binomial distribution (which is the distribution of a sum of independent and identically distributed geometric random variables). 

Tomas Garza
Mexico City (temporarily in Barcelona)

----
Gareth Russell wrote:
Can anyone tell me why Mathematica returns (1-p)/p for Mean[
GeometricDistribution[p]] and n(1-p)/p for Mean[NegativeBinomialDistribution[
p]], when all sources I have to hand (such as CRC Standard Mathematical 
Formulae) give these as 1/p and n/p respectively? The variance expressions 
agree with CRC, it's just the means that are different. 




  • Prev by Date: Re: Appearance of Pasted Text in Input Cells
  • Next by Date: Re: Sequence of functions
  • Previous by thread: Mean of Geometric and Negative Binomial distributions
  • Next by thread: Re: Mean of Geometric and Negative Binomial distributions