Prob & Stats, Lec 19B: Binomial Distribution Method of Moments Estimator for p (M.O.M. Estimator)

What is the Method of Moments (M.O.M) estimator for the parameter p of a Binomial distribution B(n,p)? We use the fact that the mean (expected value) of X ∼ B(n,p) is μ = E[X] = np. On each side of this equation relating parameters, we replace them with their estimators: X̄ = M1 = np̂. Then we solve for p̂ to get p̂ = X̄/n. If the random sample X1, X2,..., Xm has sample size m, this can be written as p̂ = sum(Xi)/(mn). We can also say p̂ is an unbiased estimator for p. That is, the expected value E[p̂]=p (the expected value of the statistic equals the parameter value.

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