Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T04:39:28.827Z Has data issue: false hasContentIssue false
  • English
  • Français

A study of the variance of mortality rates

Published online by Cambridge University Press:  20 April 2012

R. H. Daw
Get access Rights & Permissions [Opens in a new window]

Extract

Some 20 to 30 years ago considerable progress was made in understanding the variance of mortality rates and, for assured lives data, the effect on it of the presence of duplicate policies, e.g. Redington and Michaelson (1940), Seal (1941, 1947, 1948 and 1949), Daw (1945 and 1951), Vajda (1945), Solomon (1948), Beard (1951), Jager (1953) and Continuous Mortality Investigation (C.M.I.) (1957). I have the impression that since that time this understanding has tended to regress. For example it is disappointing to find that the whole course of reading on the analysis of mortality data makes practically no mention of the effect of duplicate policies in increasing the variance of mortality rates. Yet this is a matter which can have a substantial effect on the results of testing a mortality table graduation as is recognized in C.M.I. (1974). It is salutory to find that G. H. Hardy (1882) was aware that the presence of duplicates increased the variance although he did not express it in quite that way.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 101 , Issue 3 , December 1974 , pp. 415 - 434
Copyright
Copyright © Institute and Faculty of Actuaries 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aitken, A. C. Statistical Mathematics. London: Oliver and Boyd, 1939.Google Scholar
Beard, R. E. Some notes on graduation. J.I.A. 1951, 77, 382.Google Scholar
Commonwealth Actuary. Australian Life Tables 1960–1962. Commonwealth Bureau of census and statistics, Canberra, 1965.Google Scholar
Continuous investigation into the mortality of assured lives. Memorandum on a special enquiry into the distribution of duplicate policies. J.I.A. 1957, 83, 34.Google Scholar
C.M.I. Considerations affecting the preparation of standard tables of mortality. J.I.A. 1974, 101, 133.Google Scholar
Daw, R. H. On the validity of statistical tests of the graduation of a mortality table. J.I.A. 1945, 72, 174.Google Scholar
Daw, R. H. Duplicate policies in mortality data. J.I.A. 1951, 77, 261.Google Scholar
Daw, R. H. Some statistical aspects of mortality from degenerative heart disease. J.I.A. 1954, 80, 69.Google Scholar
Derksen, J. B. D. The calculation of mortality rates in the construction of life tables. A mathematical statistical study. Population Studies 1948, 1, 457.CrossRefGoogle Scholar
Hardy, G. H. On the mortality observed amongst the various classes of bonus policies in the British Empire Mutual Assurance Company. J.I.A. 1882, 23, 1.Google Scholar
Jager, J. De. Stochastical investigations on mortality tables. Het Verzekerings-Archief, Actuarieel Bijvoegsel 1953, 30, 76.Google Scholar
Netherlands Central Bureau of Statistics. Life tables for the Netherlands 1961–1965. (1967)Google Scholar
Netherlands Central Bureau of Statistics. Life tables for the Netherlands 1966–1970. (1972).Google Scholar
Pollard, A. H. Random mortality fluctuations and the binomial hypothesis. J.I.A. 1970, 96, 251.Google Scholar
Pollard, A. H. Correspondence. J.I.A. 1971, 98, 91.Google Scholar
Redington, F. M. and Michaelson, R. L. An aspect of the a priori probability theory of mortality. Trans. Twelfth Int. Cong. Act., Lucerne, 1940, I, 225.Google Scholar
Seal, H. L. Tests of a mortality table graduation. J.I.A. 1941, 71, 5.Google Scholar
Seal, H. L. A probability distribution of deaths at age x when policies are counted instead of lives. Skand. Actuar. 1947, 30, 18.CrossRefGoogle Scholar
Seal, H. L. The probability of decrements from a population. A study in discrete random processes. Skand. Actuar. 1948, 31, 14.CrossRefGoogle Scholar
Seal, H. L. Mortality data and the binomial law. Skand. Actuar. 1949, 32, 188.Google Scholar
Solomon, L. The analysis of heterogeneous mortality data. J.I.A. 1948, 74, 94.Google Scholar
Vajda, S. The analysis of variance of mortality rates. J.I.A. 1945, 72, 240.Google Scholar