  Quantification is a supervised machine learning task, focused on estimating
the class prevalence of a dataset rather than labeling its individual
observations. We introduce Continuous Sweep, a new parametric binary quantifier
inspired by the well-performing Median Sweep. Median Sweep is currently one of
the best binary quantifiers, but we have changed this quantifier on three
points, namely 1) using parametric class distributions instead of empirical
distributions, 2) optimizing decision boundaries instead of applying discrete
decision rules, and 3) calculating the mean instead of the median. We derive
analytic expressions for the bias and variance of Continuous Sweep under
general model assumptions. This is one of the first theoretical contributions
in the field of quantification learning. Moreover, these derivations enable us
to find the optimal decision boundaries. Finally, our simulation study shows
that Continuous Sweep outperforms Median Sweep in a wide range of situations.
