Quantifying the privacy loss of a privacy-preserving mechanism on potentially sensitive data is a complex and well-researched topic; the de-facto standard for privacy measures are ε-differential privacy (DP) and its versatile relaxation (ε, δ)-approximate differential privacy (ADP). Recently, novel variants of (A)DP focused on giving tighter privacy bounds under continual observation. In this paper we unify many previous works via the privacy loss distribution (PLD) of a mechanism. We show that for non-adaptive mechanisms, the privacy loss under sequential composition undergoes a convolution and will converge to a Gauss distribution (the central limit theorem for DP). We derive several relevant insights: we can now characterize mechanisms by their privacy loss class, i.e., by the Gauss distribution to which their PLD converges, which allows us to give novel ADP bounds for mechanisms based on their privacy loss class; we derive exact analytical guarantees for the approximate randomized response mechanism and an exact analytical and closed formula for the Gauss mechanism, that, given ε, calculates δ, s.t., the mechanism is (ε, δ)-ADP (not an over-approximating bound).
 M. Abadi A. Chu I. Goodfellow H. B. McMahan I. Mironov K. Talwar and L. Zhang “Deep Learning with Differential Privacy” in Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security (CCS). ACM 2016 pp. 308–318.
 M. Abramowitz and I. A. Stegun Handbook of Mathematical Functions with Formulas Graphs and Mathematical Tables 1st ed. New York: Dover 1972.
 B. Balle G. Barthe and M. Gaboardi “Privacy amplification by subsampling: Tight analyses via couplings and divergences” in Neural Information Processing Systems (NIPS) 2018.
 B. Balle and Y. Wang “Improving the gaussian mechanism for differential privacy: Analytical calibration and optimal denoising” in Proceedings of the 35th International Conference on Machine Learning (ICML) 2018 pp. 403–412.
 P. Billingsley Probability and measure. John Wiley & Sons 2008.
 V. I. Bogachev Measure theory. Springer Science & Business Media 2007 vol. 1.
 M. Bun and T. Steinke “Concentrated Differential Privacy: Simplifications Extensions and Lower Bounds” in Theory of Cryptography (TCC). Springer 2016 pp. 635–658.
 I. Dinur and K. Nissim “Revealing Information While Preserving Privacy” in Proceedings of the Twenty-second ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS). ACM 2003 pp. 202–210.
 C. Dwork K. Kenthapadi F. McSherry I. Mironov and M. Naor “Our Data Ourselves: Privacy Via Distributed Noise Generation” in Advances in Cryptology - EURO-CRYPT 2006. Springer 2006 pp. 486–503.
 C. Dwork and A. Roth “The Algorithmic Foundations of Differential Privacy” Foundations and Trends® in Theoretical Computer Science vol. 9 no. 3–4 pp. 211–407 2014.
 C. Dwork and G. N. Rothblum “Concentrated Differential Privacy” CoRR vol. abs/1603.01887 2016.
 U. Erlingsson V. Pihur and A. Korolova “Rappor: Randomized aggregatable privacy-preserving ordinal response” in Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security (CCS). ACM 2014.
 M. Götz A. Machanavajjhala G. Wang X. Xiao and J. Gehrke “Privacy in search logs” CoRR vol. abs/0904.0682 2009.
 B. Gough GNU Scientific Library Reference Manual - Third Edition 3rd ed. Network Theory Ltd. 2009.
 P. Kairouz S. Oh and P. Viswanath “The composition theorem for differential privacy” IEEE Transactions on Information Theory vol. 63 no. 6 pp. 4037–4049 2017.
 J. W. Lindeberg “Eine neue herleitung des exponentialgesetzes in der wahrscheinlichkeitsrechnung” Mathematische Zeitschrift vol. 15 no. 1 pp. 211–225 1922.
 A. Machanavajjhala D. Kifer J. Abowd J. Gehrke and L. Vilhuber “Privacy: Theory meets practice on the map” in 2008 IEEE 24th International Conference on Data Engineering April 2008 pp. 277–286.
 S. Meiser “Approximate and Probabilistic Differential Privacy Definitions” https://eprint.iacr.org/2018/277 2018.
 S. Meiser and E. Mohammadi “Tight on Budget? Tight Bounds for r-Fold Approximate Differential Privacy” in Proceedings of the 25th ACM Conference on Computer and Communications Security (CCS). ACM 2018.
 I. Mironov “Rényi Differential Privacy” in Proceedings of the 30th IEEE Computer Security Foundations Symposium (CSF). IEEE 2017 pp. 263–275.
 J. Murtagh and S. Vadhan “The complexity of computing the optimal composition of differential privacy” in Proceedings Part I of the 13th International Conference on Theory of Cryptography (TCC). Springer 2016 pp. 157–175.
 I. Pinelis “Chapter 4 - on the nonuniform berry–esseen bound” in Inequalities and Extremal Problems in Probability and Statistics. Academic Press 2017 pp. 103 – 138.
 EU Regulation “European data protection regulation (GDPR)” Off J Eur Union vol. L119 pp. 1–88 4th May 2016.
 D. Sommer A. Dhar L. Malitsa E. Mohammadi D. Ronzani and S. Capkun “Anonymous Communication for Messengers via “Forced” Participation” Technical report available under https://eprint.iacr.org/2017/191 2017.
 S. Vadhan G. N. Rothblum and C. Dwork “Boosting and differential privacy” in 2010 IEEE 51st Annual Symposium on Foundations of Computer Science (FOCS) 2010 pp. 51–60.
 J. van den Hooff D. Lazar M. Zaharia and N. Zeldovich “Vuvuzela: Scalable private messaging resistant to traffic analysis” in Proceedings of the 25th Symposium on Operating Systems Principles (SOSP). ACM 2015 pp. 137–152.
 Y.-X. Wang B. Balle and S. Kasiviswanathan “Subsampled Rényi differential privacy and analytical moments accountant” arXiv preprint arXiv:1808.00087 2018.