  The problem of distinct value estimation has many applications. Being a
critical component of query optimizers in databases, it also has high
commercial impact. Many distinct value estimators have been proposed, using
various statistical approaches. However, characterizing the errors incurred by
these estimators is an open problem: existing analytical approaches are not
powerful enough, and extensive empirical studies at large scale do not exist.
We conduct an extensive large-scale empirical study of 11 distinct value
estimators from four different approaches to the problem over families of
Zipfian distributions whose parameters model real-world applications. Our study
is the first that \emph{scales to the size of a billion-rows} that today's
large commercial databases have to operate in. This allows us to characterize
the error that is encountered in real-world applications of distinct value
estimation. By mining the generated data, we show that estimator error depends
on a key latent parameter --- the average uniform class size --- that has not
been studied previously. This parameter also allows us to unearth error
patterns that were previously unknown. Importantly, ours is the first approach
that provides a framework for \emph{visualizing the error patterns} in distinct
value estimation, facilitating discussion of this problem in enterprise
settings. Our characterization of errors can be used for several problems in
distinct value estimation, such as the design of hybrid estimators. This work
aims at the practitioner and the researcher alike, and addresses questions
frequently asked by both audiences.
