Fisher’s Noncentral Hypergeometric Distribution for Population Size Estimation

Fisher’s noncentral hypergeometric (FNCH) distribution naturally suits biased sampling processes. Indeed, this distribution describes a biased urn experiment where balls of different colors are associated with different weights. Despite its potentiality, FNCH distribution has never been applied to official statistics problems, such as the size estimation of heterogeneous populations. Such underuse is mainly due to the computational burden given by its probability mass function, which makes the evaluation of the likelihood function challenging. We present a methodology to estimate the posterior distribution of FNCH parameters, exploiting extra-experimental information and the computational efficiency of MCMC methods. We assess the robustness to weights prior specifications via simulation studies.