  We consider the problem of the private release of statistics (like aggregate
payrolls) where it is critical to preserve the contribution made by a small
number of outlying large entities. We propose a privacy formalism, per-record
zero concentrated differential privacy (PzCDP), where the privacy loss
associated with each record is a public function of that record's value. Unlike
other formalisms which provide different privacy losses to different records,
PzCDP's privacy loss depends explicitly on the confidential data. We define our
formalism, derive its properties, and propose mechanisms which satisfy PzCDP
that are uniquely suited to publishing skewed or heavy-tailed statistics, where
a small number of records contribute substantially to query answers. This
targeted relaxation helps overcome the difficulties of applying standard DP to
these data products.
