We study the problem of learning exponential distributions under differential privacy. Given n i. i. d. \ samples from Exp (λ), the goal is to privately estimate λ so that the learned distribution is close in total variation distance to the truth. We present two complementary pure DP algorithms: one adapts the classical maximum likelihood estimator via clipping and Laplace noise, while the other leverages the fact that the (1-1/e) -quantile equals 1/λ. Each method excels in a different regime, and we combine them into an adaptive best-of-both algorithm achieving near-optimal sample complexity for all λ. We further extend our approach to Pareto distributions via a logarithmic reduction, prove nearly matching lower bounds using packing and group privacy Karwa2017FiniteSD, and show how approximate (ε, δ) -DP removes the need for externally supplied bounds. Together, these results give the first tight characterization of exponential distribution learning under DP and illustrate the power of adaptive strategies for heavy-tailed laws.
Mahpud et al. (Wed,) studied this question.