  The $t$-digest is a data structure that can be queried for approximate
quantiles, with greater accuracy near the minimum and maximum of the
distribution. We develop a $t$-digest variant with accuracy asymmetric about
the median, thereby making possible alternative tradeoffs between computational
resources and accuracy which may be of particular interest for distributions
with significant skew. After establishing some theoretical properties of scale
functions for $t$-digests, we show that a tangent line construction on the
familiar scale functions preserves the crucial properties that allow
$t$-digests to operate online and be mergeable. We conclude with an empirical
study demonstrating the asymmetric variant preserves accuracy on one side of
the distribution with a much smaller memory footprint.

Data Structures and Algorithms