Barry S. Griffin, Richard G. Krutchkoff, An Empirical Bayes Estimator for P [Success] in the Binomial Distribution, Sankhyā: The Indian Journal of Statistics, Series B (1960-2002), Vol. 33, No. 3/4 ...

Estimating the number, n, of trials, given a sequence of independent success counts obtained by replicating the n-trial experiment is less studied and a considerably harder problem than estimating p ...