Re: Is n a parameter of a binomial distribution?
- From: "Anon." <bob.ohara@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 19 Oct 2007 16:08:55 +0300
vontressms@xxxxxx wrote:
On Oct 18, 1:23 pm, Vinayak Rao <vinayak....@xxxxxxxxx> wrote:Of course, one could write a binomial as two exponentials, in which case n is the sum of both, and hence is a statistic.Hi,
Is the number of experiments 'n' a parameter of the binomial
distribution
p(k|n,p) = nCk p^k (1-p)^(n-k) ?
The answer would seem to be 'yes' almost by definition, but if I
express the binomial distribution in the "exponential family form", it
has only 1 natural parameter log(p/(1-p)). If n were a parameter,
would this mean that the binomial belongs to the exponential family
only w.r.to parameter p (and not n)?
Vinayak
Vinayak,
n is not usually considered a parameter in the binomial
distribution. It is a fixed number by the design of the experiment. We
usually estimate p in a given number of n trials where there are k
successes, and k is a random variable ranging between zero and n.
Your expression of the density as a member of the exponential family
is another reason why n is not usually considered a "parameter".
Bob
--
Bob O'Hara
Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
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- Is n a parameter of a binomial distribution?
- From: Vinayak Rao
- Re: Is n a parameter of a binomial distribution?
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- Is n a parameter of a binomial distribution?
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