2 replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/ edited Apr 13 '17 at 12:44 In the process of answering this: http://stats.stackexchange.com/questions/123367/estimating-parameters-for-a-binomial/123748?noredirect=1#comment235901_123748Estimating parameters for a binomial I stumbled over this paper: Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribution. Jasa 1981. which gives an example where method of moments, at least in some cases, beats maximum likelihood. The problem is estimation of $$N$$ in the binomial distribution $$\text{Bin}(N,p)$$ where both parameters are unknown. It appears for example in trying to estimate animal abundance when you cannot see all the animals, and the sighting probability $$p$$ also is unknown. In the process of answering this: http://stats.stackexchange.com/questions/123367/estimating-parameters-for-a-binomial/123748?noredirect=1#comment235901_123748 I stumbled over this paper: Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribution. Jasa 1981. which gives an example where method of moments, at least in some cases, beats maximum likelihood. The problem is estimation of $$N$$ in the binomial distribution $$\text{Bin}(N,p)$$ where both parameters are unknown. It appears for example in trying to estimate animal abundance when you cannot see all the animals, and the sighting probability $$p$$ also is unknown. In the process of answering this: Estimating parameters for a binomial I stumbled over this paper: Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribution. Jasa 1981. which gives an example where method of moments, at least in some cases, beats maximum likelihood. The problem is estimation of $$N$$ in the binomial distribution $$\text{Bin}(N,p)$$ where both parameters are unknown. It appears for example in trying to estimate animal abundance when you cannot see all the animals, and the sighting probability $$p$$ also is unknown. 1 answered Nov 13 '14 at 10:43 kjetil b halvorsen 38.3k99 gold badges9292 silver badges297297 bronze badges In the process of answering this: http://stats.stackexchange.com/questions/123367/estimating-parameters-for-a-binomial/123748?noredirect=1#comment235901_123748 I stumbled over this paper: Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribution. Jasa 1981. which gives an example where method of moments, at least in some cases, beats maximum likelihood. The problem is estimation of $$N$$ in the binomial distribution $$\text{Bin}(N,p)$$ where both parameters are unknown. It appears for example in trying to estimate animal abundance when you cannot see all the animals, and the sighting probability $$p$$ also is unknown.