This paper is concerned with the application of probability theory to sickness. An attempt is made to explore the form, and in particular the standard deviation, of the distribution of the sickness experienced by a body of lives. It appears that, in the past, none but empirical investigations have been made in this field, the theoretical foundation being entirely lacking. The only exceptions are Sir George Hardy's paper in J.I.A. Vol. XXVII, and the paper in J.S.S. Vol. VII by R. E. Beard on The standard deviation of the distribution of sickness. This statistic, as Beard points out, appears to have been practically ignored by British actuaries hitherto.

This paper is founded as factually as possible on a case which arose in practice. Originally it was intended to present the paper as a collection of the actual documents, letters, valuation reports and so on, with only a minimum of outright description. Unfortunately, it gradually became clear that the result would not be suitable and practically the whole has been rewritten. Nevertheless, an attempt has been made to retain as much of the atmosphere as possible.

Several methods of forecasting mortality have from time to time been suggested. Some of them have, however, only been applied to the statistics of one or two countries and, while they have been found to be satisfactory in these cases, we cannot justifiably say that the assumptions on which they are based are universally valid. In §§ 3–7 these standard methods of mortality forecasting will, with necessary modifications, be applied to Australian data. These sections do not, therefore, involve anything in the way of new principle, but, being applications of old methods to new data, they should make a further contribution to our knowledge of the validity of the assumptions on which these standard methods are based. In § 9 a further method of forecasting will be described, and in § 10 the results obtained by the several methods will be compared.

This paper is the record of an attempt by an ordinary actuary, who entered the profession in days when statistics were but a nugatory ingredient in the examination syllabus, to get a little clearer in his mind about some of the similarities and differences between the traditional technique of the actuary and the methods which have been developed for dealing with statistical material in other fields. It seemed that the result might be of some general interest, and it is from this point of view that the paper is submitted to the Institute.