Re: Is n a parameter of a binomial distribution?

On Oct 26, 1:35 pm, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:
In article <1193247073.540767.154...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,





<vontres...@xxxxxx> wrote:
On Oct 24, 10:53 am, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:
In article <1192797455.065283.3...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<vontres...@xxxxxx> wrote:
On Oct 18, 1:23 pm, Vinayak Rao <vinayak....@xxxxxxxxx> wrote:
Anything which can be computed from a probability
distribution is a parameter, so n is a parameter.
There is considerable information on the estimation
of n if p is known, and also if p is unknown.
A set of such parameters can be called the parameters
of a family of distributions if their values determine
the distribution. Usually, n and p are the parameters.
The binomial distribution belongs to the exponential
family with respect to p, but not with respect to n.
One gets a rather interesting estimation problem if
the parameters used are h = 1/n and np. In this case,
one gets the binomial distribution if 1/h is a positive
integer, Poisson if h = 0, and negative binomial if h < 0.
Herman,
I will agree with you that anything that anything which can be
computed from a probability distribution is a parameter, so n is a
parameter if it has a probability distribution.

Any parameter of an distribution is function of that
distribution, and that is all. For a binomial
ditribution, the usual stated parameters are n and p,
but others can be used. For a given distribution,
there is nothing random about the distribution.

There is also the inference problem about parameters.
It may be that n is by far the more important parameter
than p. For example, suppose that one wants to test
whether p=.49 or p=.51. Suppose that if p=.49, items
come regularly once a second, and if p=.51, regularly
once an hour. Instead of fixing n, I suggest we fix
the time and go by how many have been seen.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558- Hide quoted text -

- Show quoted text -

Herman,
That is an interesting problem that I've never had to work with
before. It's pretty clear that you can get an MLE for N using x and a
prespecified p. How would you select p from your two choices?
Mark

.

Relevant Pages

  • Re: Pigeons, People, and Priors
    ... the variance of the probability generator go to zero you have a continuum ... a random-interval 60 s schedule is not. ... The Exponential Distribution ... I probably should have used the phrase "statistical learning theory" rather ...
    (comp.ai.philosophy)
  • Re: Probabilty Question
    ... I think that you asked whether you can tell what the heads probability ... paramater is in the interval. ... "prior" distribution on the value of the paramater. ... Estimation is a huge area of statistice, ...
    (sci.math)
  • Re: So called "stimulus/response" models
    ... Instead of answering to each misunderstood, ironic and out of context ... Sorry, you exhibit a simplistic view of probability theory, and an even more ... of acquiring the consequences of responses. ... distribution over consequences of a given act. ...
    (comp.ai.philosophy)
  • Re: behavior as mapping
    ... estimating a probability distribution, the distribution ... sequence with equal probability - since you have microsecond temporal ... reduction of the entropy Pto the entropy P ... If there were 4 genes we would need 2 bits of binding site info. ...
    (comp.ai.philosophy)
  • Re: Bill Reid, Kelly Criterion
    ... about logs; if a person is talking about a percentage change in the ... probability of going broke the more they trade. ... adjustment (which is the one which allows any distribution which is ...
    (misc.invest.stocks)