Abstract

In this paper an attempt is made to refine the method of fitting the Gompertz function to the cumulative fertility rates by using iterative techniques. The method is tested with the historical data series for the Canadian population. The demographic implication of the parameters of the Gompertz function as fitted to the fertility distribution is examined, and the usefulness of the method in projecting future fertility trends is studied. The Makeham function is also fitted to the fertility distribution by the same iterative technique, and the relative efficiency of this function is compared with that of the Gompertz.

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References

Avery, Roger C. 1970. Graduation of age-speeific fertility rates. Paper presented at the Third Conference on the Mathematics of Population, July 19–24, 1970, The University of Chicago.
Brass, W. (
1960
).
Graduation of fertility distribution by polynomials functions
.
Population Studies
,
14
(
2
),
148
162
. 10.2307/2172011
Projection of Incomplete Cohort Fertility for Canada by Means of the Gompertz Function, by A. Romaniuk and S. M. Tanny
. (
1969
).
Ottawa
:
Census Division
.
Life Tables, Canada and the Provinces (1965–1967)
. (
1971
).
Ottawa
:
Queen’s Printer
.
1966 Census of Canada. Vol. I, Population
. (
1971
).
Ottawa
:
Queen’s Printer
.
Forsythe, C. H. (
1924
).
Mathematical Theory of Life Insurance
.
London
:
John Wiley and Sons
.
Keyfitz, N. (
1968
).
Introduction to the Mathematics of Population
.
Reading, Mass.
:
Addison-Wesley
.
Martin, M. D. P. (
1967
). Une application des fonctions de Gompertz à l’étude de la fécondité d’une cohorte.
Population
,
22
(
6
),
1085
1096
. 10.2307/1527604
Miller, M. D. (
1946
).
Elements of Graduation
.
Philadelphia
:
American Institute of Actuaries
.
Romaniuk, A. (
1969
).
The unpublished data series in his collection
.
Ottawa
:
Population Estimates and Projections Section, Census Division, Dominion Bureau of Statistics
.
Wunsch, G. (
1966
). Courbes de Gompertz et perspectives de fécondité.
Recherches Economiques de Louvain
,
32
(
6
),
457
468
.