Estimation of the parameters of the binomial distribution in a model of mixture
A. Shcherbina · Theory of Probability and Mathematical Statistics · 2013
A model for observations sampled from a two component mixture is considered. Each object is associated with a certain numerical characteristic that may assume two values, namely zero (failure) or one (success) with identical probabilities for all objects in every class. Probabilities for these values are constant for all objects from the same component. The total numbers of objects of the first and second classes in groups as well as their characteristics are known. We study the problem of estimation of success probabilities for both components. We solve the problem by using the maximum likelihood method. We prove that the estimator is consistent and asymptotically normal. We apply the results obtained in the paper to a problem in genetics. An explicit form of the estimator and the asymptotic dispersion matrix is presented.