Methods, apparatus, and systems are disclosed for determining census-level audience metrics across demographics. An example apparatus disclosed herein includes a distribution parameter solver to initialize distribution parameter values for a probability of an individual within a demographic being included in a subscriber audience for the demographic and having a first average impression duration, the subscriber audience having a first subscriber audience size, a divergence parameter solver to determine divergence parameter values between (i) the subscriber audience size and the first impression duration and (ii) a census-level audience size and a second impression duration based on the initialized distribution parameter values, and a search space identifier to identify a search space within bounds based on a census-level total impression count and a census-level total impression duration, the search space to define a range including an equality constraint.
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