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On Graduation By Mathematical Formula


In the course of work undertaken as members of the Executive Committee of the Continuous Mortality Investigation Bureau in the preparation of graduated tables of mortality for the experiences of 1979–82, we have had occasion to make use of and develop a number of statistical techniques with which actuaries may not be familiar, and which are not fully discussed in the current textbook by Benjamin & Pollard (1980), though some of them have been referred to in previous papers by the CMI Committee (1974, 1976). We therefore felt that it would be useful to the profession if we were to present these methods comprehensively in one paper. We do this with the permission of the other members of the CMI Committee, who do not, however, take responsibility for what follows, whether good or bad.

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H. Akaike (1978). On the likelihood of a Time-series Model. The Statistician, 27, 217.

H. Akaike (1985). ‘Prediction and Entropy’ in A Celebration of Statistics, edited by C. Atkinson & S. E. Fienberg , Springer Verlag, New York.

C. de Boor (1978). A Practical Guide to Splines. Springer-Verlag. New York

J. Durbin (1973). Distribution Theory for Tests Based on the Sample Distribution Function. Society for Industrial and Applied Mathematics, Philadelphia, PA.

R. V. Hogg & S. A. Klugman (1984). Loss Distributions. John Wiley, New York.

J. A. Nelder & R. Mead (1965). A simplex method for function minimization. Computer Journal, 7, 308.

C. R. Rao (1973). Linear Statistical Inference and its Applications, Second Edition. John Wiley, New York.

B. L. Van der Waerden (1969). Mathematical Statistics. George Allan and Unwin, London.

(3) N. E. Breslow , J. H. Lubin , P. Marek ,: (1983) Multiplicative models and cohort analysis. J. Am. Stat. Assoc. 78:1–12.

(6) E. L. Kaplan , P. Meier (1958) Non-parametric estimation from incomplete observations. J. Am. Stat. Assoc. 53: 459–481.

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Transactions of the Faculty of Actuaries
  • ISSN: 0071-3686
  • EISSN: 2058-1033
  • URL: /core/journals/transactions-of-the-faculty-of-actuaries
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