The paper presents a new method for empirical assessment of tsunami recurrence parameters, namely the mean tsunami activity rate λT , the Soloviev–Imamura frequency–magnitude power law bT -value, and the coastline-characteristic, maximum possible tsunami intensity imax . The three coastline-characteristic recurrence parameters are estimated locally by maximum likelihood techniques using only tsunami event catalogues. The method provides for incompleteness of the tsunami catalogue, uncertainty in the tsunami intensity determination, and uncertainty associated with the parameters in the applied tsunami occurrence models. Aleatory and epistemic uncertainty is introduced in the tsunami models by means of the use of mixture distributions. Both the mean tsunami activity rate λT of the Poisson occurrence model, and the bT -value of the Soloviev–Imamura frequency–intensity power law are random variables. The proposed procedure was applied to estimate the probabilities of exceedance and return periods for tsunamis in the tsunamigenic regions of Japan, Kuril–Kamchatka, and South America.