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A Measure of Smoothness and Some Remarks on a New Principle of Graduation

Published online by Cambridge University Press:  18 August 2016

M. T. L. Bizley
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Extract

The achievement of smoothness is one of the main purposes of graduation. Smoothness, however, has never been defined except in terms of concepts which themselves defy definition, and there is no accepted way of measuring it. This paper presents an attempt to supply a definition by constructing a quantitative measure of smoothness, and suggests that such a measure may enable us in the future to graduate without prejudicing the process by an arbitrary choice of the form of the relationship between the variables.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 84 , Issue 2 , September 1958 , pp. 125 - 165
Copyright
Copyright © Institute and Faculty of Actuaries 1958

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References

page 133 note * We are concerned with curves which actuaries use in practice and not with continuous curves in general; thus we assume that our curve possesses a tangent at every point. Similarly, we assume that the continuous functions with which we deal in this paper are always differentiable.