On Identifiability in Weighted DistributionsUsing Generalized Maximum LikelihoodEstimation

In this research, the generalized maximum likelihood estimator(GMLE) is used to investigate the parameters estimation forweighted distributions. There exist situations where the random samplefrom the population of interest is not available due to the datahaving unequal probabilities of entering the sample. The method ofweighted distributions models the certainty of the probabilities of theevents as observed and recorded. It is shown that if the mechanismof sample selection is known up to one unknown parameter, the maximumlikelihood estimator (MLE) would be unidentifiable when theconjugate weight function is used. This problem is solved by additionof a prior distribution on model parameters yielding the GMLEswhich are identifiable. We also propose the GMLEs for negative exponential,normal and Poisson weighted distributions when MLEs areunidentifiable