Estimation of the Parameternin the Binomial Distribution

Let Xi, … Xr, be independent B(n,p) random variables. In this paper n is estimated with known p. The MLE is developed and shown to be consistent in a relative sense and asymptotically normal. Motivated by Yi = Xi/q we consider Y1, … Yr independent N(μ,μ) and examine three estimates of μ; (i) the MVUE, (ii) the MLE, and (iii) . These are shown to be asymptotically equivalent.