1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fisher's Approximation of a Binomial Distribution

  1. Nov 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose that X is the number of successes in a Binomial experiment with n trials and
    probability of success θ/(1+θ), where 0 ≤ θ < ∞. (a) Find the MLE of θ. (b) Use Fisher’s
    Theorem to find the approximate distribution of the MLE when n is large.

    2. Relevant equations

    Fisher's Approximation in its full form can be see here:


    3. The attempt at a solution

    The MLE is easy enough to find, but the question I have is one about Fisher's approximation. In the formula for calculating the 1/(tau)^2 portion of the variance, note that you must use the distribution of only one of X1, X2, etc. This makes plenty of sense if you have a collection of some other kinds of i.i.d. variables (normal, exponential, etc.), but what about if you have one binomial experiment made up of n trials?

    What does this imply in the binomial case? Do I calculate 1/(tau)^2 using just the entire binomial distribution given in the problem, or do I use something else (one bernoulli trial, maybe)? Thanks!
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted