During 1961 and 1962 a Swedish governmental committee carried out experiments with temporary speed limits on rural roads. The purpose was to study the effect of such speed limits, especially their effect on the number of road accidents. To compare periods with and without speed limits it is important to isolate the speed limit factor, and for this reason other relevant factors were also considered. An estimate was made by a traffic census, of the number of vehicle-kilometers travelled daily. The analysis of the data utilized among other things a model for stating the relationship between the number of accidents and the amount of traffic. According to this model the number of accidents on a certain day is assumed to be normally distributed with a mean depending in a linear way on the traffic that day, the variance being constant and the same for all the days considered. The number of accidents for different days were further assumed to be stochastically independent. (See Traffic Safety Committee, 1965; Erlander and Gustavsson, 1965.) The aim of the present paper is to study this model in somewhat more detail and also to study other models on the relationship between road accidents and traffic, in which the daily number of accidents is assumed to have a Poisson distribution. The present study will incorporate some of the data collected in connection with the experiments with speed limits mentioned above.
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