obtaining a first vector of counts indicative of digital impressions logged by a database proprietor, wherein the first vector of counts represents counts within a plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the database proprietor to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;

obtaining a second vector of counts indicative of digital impressions logged by an audience measurement entity, wherein the second vector of counts represents counts within the plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the audience measurement entity to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;

obtaining a first variance of the first vector of counts;

determining a second variance of the second vector of counts;

determining a covariance of the first vector of counts and the second vector of counts;

determining a number of duplications between the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first variance, the second variance, the covariance, a first cardinality of the digital impressions logged by the database proprietor, and a second cardinality of the digital impressions logged by the audience measurement entity;

determining a unique audience for a combination of the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first cardinality, the second cardinality, and the number of duplications; and

transmitting the unique audience to a third-party.