This paper examines the statistical properties of estimates of fatal accident rates, mean fatalities per accident, and fatality rates when these estimates are based on past accident data. The statistical properties are illustrated by two long-term transport fatal accident datasets from Great Britain, the principal one for railways and the other for roads, chosen to provide a statistical contrast. In both modes, the accident rates have fallen substantially over the long term. Two statistical estimates of current accident and fatality rates are presented for each dataset, one based only on recent data and the other based on estimates of long-term trends. The trend-based estimate is preferred for train accidents because this makes maximum use of the limited and variable data; the recent data are preferred for road accidents because this avoids unnecessary dependence on modelling the trends. For train accidents, the estimated fatality rate based on past accidents is compared with an estimate produced by the railway industry using a risk model. The statistical estimate is less than half the industry's estimate, and the paper concludes that the statistical estimate is to be preferred.