  We introduce a family of information leakage measures called maximal
$\alpha,\beta$-leakage, parameterized by real numbers $\alpha$ and $\beta$. The
measure is formalized via an operational definition involving an adversary
guessing an unknown function of the data given the released data. We obtain a
simple, computable expression for the measure and show that it satisfies
several basic properties such as monotonicity in $\beta$ for a fixed $\alpha$,
non-negativity, data processing inequalities, and additivity over independent
releases. Finally, we highlight the relevance of this family by showing that it
bridges several known leakage measures, including maximal $\alpha$-leakage
$(\beta=1)$, maximal leakage $(\alpha=\infty,\beta=1)$, local differential
privacy $(\alpha=\infty,\beta=\infty)$, and local Renyi differential privacy
$(\alpha=\beta)$.
