Credibility and Automobile Rate Making [Discussion]

The casualty actuary in his use of statistical data finds himself in a somewhat different position from most other workers. They may have certain data of the past, for example a series showing the current rate of interest monthly over a period of years. They may wish to project the series into the future and want to know from the review of past data, approximately how accurate their forecast will be. They may have correlating data to work from, or as with the life insurance actuary something approximating a natural law to use as a graduation formula. He must forecast costs and recognize as fine distinctions as possible with the closest accuracy obtainable. For them the problem is, "How accurate is the result I can get from the data in hand?" For him it is often, "How much data must I have to be right within a given margin"? Perhaps it is because this heavy responsibility is not shared by others that the literature of statistics has not discussed the problem more fully. It seems to be among the most difficult in the field of mathematical statistics and probability.