[R] binom and negbinom

[Troels Ring]

Dear friends. In Carlin and Louis "Bayes and emperical Bayes methods.." 
1996 the classical example of 12 independent tosses of a fair coin 
producing 9 heads and 3 tails is given. If the situation is seen as a fixed 
sample of 12, a binomial lieklihood is used, and Carlin et al reports a 
probability of 0.075.
Using sum(dbinom(9:12,12,.5)) I obtain 0.073
Likewise, if the experiment is seen as continuing until 3 tails are noted, 
a negative binomial is used, and the authors find P = 0.0325, whereas 
sum(dnbinom(9:1000,3,.5)) gives 0.0327.
These differences may be small - but who is right, either R or Carlin - or 
did I do it wrong ?


Best wishes

Troels 

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