Some unusual features of the likelihood function of the three-parameter lognormal distributionln(t – γ)∼N(μ, σ2) are explored. In particular, it is shown that there exist paths along which the likelihood function of any samplet1, …,tntends to ∞ as (γ, μ, σ2) approaches (t(1), – ∞, + ∞), wheret(1)is the smallest of theti, and hence that in a meaningful sense this is the maximum-likelihood estimate. Estimation is then considered from a Bayesian point of view, and some natural posterior distributions are explored. A statistical model for a point-source epidemic is presented, and the theory developed is used in estimating the time of onset and other parameters.