Small Sample Performance of Some Estimators of the Truncated Binomial Distribution

Estimation of the parameter of a binomial distribution with the zero class truncated is a classical problem in human genetics. Mathematically the problem is the estimation of p from n, independent observations with distribution, ( r s )p r q s-r /(1 - q s ) where r = 1, 2, ··· s, q = 1 - p and s ≥ 2 is a known integer. This article gives exact results which show the simple estimator of Mantel [17] to be less biased, both asymptotically and in small samples, than either the ML estimator or Weinberg's simple sib method. Its efficiency relative to the ML estimator is better in small than in large samples, ranging from 97 percent to 101 percent for the genetically important cases of p = .25 and .50. Mantel's estimator performs better than the simple sib method as an initial estimator in iterative ML scoring.