This paper attempts to give a sketch of the history and present practice of life assurance in Australia. It is not unnatural that its earliest beginnings should have been based on principles and methods which had already been developed and proved in this country. There are still many similarities, but differences have arisen in the new environment, and an examination of these differences may be of interest to members of the Society.

Little more than 100 years ago the population of the colony of New South Wales, which then included the present territories of Queensland and Victoria, was only about 250,000, yet a few provident pioneers had already formed a Mutual Society to transact life assurance. They had been appalled by the plight of the families of the early settlers who died before they had time, by other means, to make provision for their dependants.

The development of this Society was at first very slow, but it had the good fortune to have no death claims during its first three years, nor did they exceed £2500 in any of the first ten years. It was not until the introduction of the canvassing system, with the appointment of the first full-time agent in 1860, that there was any appreciable expansion. To-day that Society is the largest mutual life office in the British Commonwealth with assets of £300 millions.

The object of this paper is to discuss the main principles underlying the pattern of interest rates on government securities in this country. It does not attempt to examine the place in the yield structure of those stocks which may possess special characteristics of term or provision for repayment, etc.; and because of its concentration on general principles the complex effects of taxation have been relegated to the background. The subject is approached by the following stages:

(1) The pattern in the hypothetical case of complete certainty.

(2) The idea of a ‘normal’ pattern, i.e. in conditions of complete uncertainty.

(3) The changing pattern in conditions of varied and fluid expectations.

This is a subject which may seem a little remote from the normal run of discussions at these meetings. But with the increasing tendency for actuaries to take up posts in Government service, in industry and in commerce, in which official statistics are an everyday need, I hope that some of you, at least, will find it interesting to have this brief account of the work of a Government statistics division.

The Statistics Division forms part of the Secretaries' Office of the Board of Inland Revenue. Its primary function is to supply the Board with the figures which the Chancellor of the Exchequer needs for Budget purposes, i.e. estimates of the future yield of taxation at current levels and of the cost or yield of possible changes in rates and allowances. The whole of the year's work centres on those requirements, but in the course of it many figures useful for other purposes emerge or can be collected with little additional effort.

Following upon the growth in the number of pension funds which has occurred in recent years, employers have become increasingly concerned with the preservation of the pension rights of employees leaving their service to enter that of other employers who may even be competitors. Having accepted the obligation to provide pension benefits for his staff as a whole, an employer must decide to what extent, if any, he wishes to preserve the pension rights of transferring employees. Before reaching his decision, however, he will, if he is wise, seek the guidance of the actuary to the fund, who should be prepared to present the alternative fundamental principles and attitudes open to him. From these should follow his decision as to whether he has an obligation to preserve the pension rights of transferring members of his staff and, if they are to be preserved, how the actuary should make the relevant calculations. Whilst decisions must ultimately rest with the employer, the actuary must be fully conversant with the subject as a whole so that he can give sound advice and be able to make the necessary calculations. It is the actuary's duty to present all sides of any problems which arise in connexion with the scheme and to indicate the consequences which may result from the employer's decisions.

In recent years the statistical technique known as ‘sequential analysis’ has been developed to a considerable degree of refinement and applied in many varied fields. The technique may, however, be new to some readers, and some examples and illustrations of the application of sequential methods to data of the type encountered in actuarial work should therefore prove of interest.

The raison d'être of sequential analysis is the reduction of the average number of observations required to reach conclusions from observed data without altering the degree of reliability specified in the usual fixed sample size technique. If such a result can be achieved a saving in both time and money may be effected.

In the usual fixed-sample size techniques the size of sample necessary to achieve a given degree of reliability in the conclusions reached can be computed. However, in the course of the selection and examination of the sample it often becomes apparent, at quite an early stage, what form of conclusion is likely to be reached.

For the past few years, stimulating research has been carried out on ordered statistics. Linear combinations of the sample ordered values are used to provide estimates of parameters of the population from which the sample is drawn. Such statistics are termed systematic by Mosteller. They are in common use, because they provide simple solutions of parametric problems of statistical estimation. Often they are inefficient, but this drawback is sometimes more than offset by the ease with which the calculations are performed.

Mosteller drew attention to the possible use of the statistics Wr, which he called quasi-range of rth order and defined as

where x1, x2,…, xn are ordered observations in a sample of n from a population f(x) (x1 < x2 < … < xn). The distributions of quasiranges in samples drawn from a normal population have been studied by Godwin and Cadwell.