Curve Fitting Process Research Articles

Notes on Formula Graduation of South African 56/58 Ultimate Mortality.

1. The S.A. 56/58 Ultimate data (seeJ.I.A.Vol.87, p. 371) was originally graduated by summation formula and arising out of the discussions it was decided to attempt to fit a mathematical formula of the Perks type.2. To start with, data below age 30 were excluded.3. The generalized Perks formulawas chosen—the thought being that if some of the parameters were not needed the process of curve fitting would result in these parameters assuming small values.

GROWTH AND DECAY

The formal laws of growth and decay play an important rôle in the literature of the subject. They have been founded on theoretical ideas of the nature of both processes and have been applied later to the data gained by observation. The comparison of the formulæ with the data required a determination of the constants of those formulæ by a process of curve fitting. The accuracy of the fit has been tested by the methods developed for such purposes by the doctrine of mathematical statistics.

A Fundamental Problem in the Case Method of Instruction in Statistics

A number of problems are faced today by those who are attempting to carry instruction in business statistics beyond the stage of the elementary course in method. In the first place, students do not learn in the elementary course, to use in a practical way, their statistical technique. This observation applies equally to students who have had a thorough preparation in mathematics and to those who have not. Conversation with other teachers has led me to conclude that the failure of elementary instruction to enable the student to apply his knowledge is confined to no one course or institution. This is not intended to be critical of such courses. It is probably impossible in the brief time allotted to them to develop in the student both a knowledge of statistical technique and skill in the application of method to concrete problems. The emphasis in an elementary course must be on the nature and calculation of statistical constants, rather than on argument from those constants. The emphasis must be on statistical description rather than on statistical inference. But if the study of statistical method in training for business is to be justified, it must be carried to the point where the student will have more than a bowing acquaintance with method and will acquire facility in drawing conclusions from quantitative data. It is easy to suggest this and somewhat difficult to accomplish it. The faculty which needs to be developed in the student is something in the nature of a power to see analogies between a new situation and a previous experience. The mental processes involved are perhaps obscure, and no final answer possible as to the method by which this power can be developed. But certain conditions essential to its development can be pointed out. The most important of these conditions is that the original experience of the student must be vivid. Tell the student that when the relationship between associated variables is disturbed by many minor causes, a process of curve fitting or graduation is an appropriate method for describing the normal relationship between the variables. He would promptly forget it. Give him a concrete problem involving the same principle and he will remember provided that the illustration is a significant one. The original experience of the student will be vivid in proportion as it seems to the student to have a significant conclusion. At the present time, it is