Abstract
This paper reports the outcome of an exercise in curve fitting to annual sets of Danish age-specific fertility rates for the years 1962 to 1971 by means of least squares. Functions fitted were a cubic spline, the Hadwiger and Coale-Trussell functions, the gamma and beta densities, two versions of a polynomial, and two of Brass's relational procedures, as well as the Gompertz curve. The spline function fitted all curves far better than any of the others. The Coale-Trussell procedure and gamma density were about equal, followed by the Hadwiger function. All of these functions fit the data well. One of the polynomials fit reasonably well, but the rest of the functions were less accurate.
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References
Berge, Erling. 1974a. Analytisk glatting av fødselsrater for Norge for åra 1968 til 1972. Central Bureau of Statistics of Norway, Working Paper IO 74/24, pp. 34–50.
Berg, Erling. 1974b. Regionale variasjonar i fertiliteten i Norge omkring 1970. Central Bureau of Statistics of Norway, Working Paper IO 74/40.
Berg, Erling. 1977. The Social Ecology of Human Fertility in Norway 1970. Boston University Graduate School. Preliminary edition.
Berge, Erling, & Hoem, Jan M. (
1975
). Nokre praktiske røynsler med analytisk glatting
. Statistical Review of the Swedish National Central Bureau of Statistics III
, 13
, 294
–308
.Bloom, David E. 1980. Age Patterns of Women at First Birth. Presented to the 1980 Annual Meetings of the Population Association of America, Denver, Colorado.
Brass, W. (
1960
). The Graduation of Fertility Distributions by Polynomial Functions
. Population Studies
, 14
, 148
–162
. 10.2307/2172011Brass, W. (
1974
). Perspectives in Population Prediction: Illustrated by the Statistics of England and Wales (with Discussion)
. Journal of the Royal Statistical Society A
, 137
, 532
–583
. 10.2307/2344713Brass, W. 1978. Population Projections for Planning and Policy. Papers of the East-West Population Institute, #55. Honolulu, Hawaii.
Brouard, N. (
1977
). Evolution de la fécondité masculine depuis le début du siècle
. Population
, 32
, 1123
–1159
. 10.2307/1531392Coale, A. J., & Trussell, T. J. (
1974
). Model Fertility Schedules: Variations in the Age Structure of Childbearing in Human Populations
. Population Index
, 40
, 185
–258
. 10.2307/2733910Coale, A. J. (
1978
). Technical Note: Finding the Two Parameters that Specify a Model Schedule of Marital Fertility
. Population Index
, 44
, 203
–213
. 10.2307/2735537Danmarks Statistik. 1973. Befolkningens bevaegelser 1971. Statistiske Meddelelser 1973:10.
Duchêne, J., & Gillet-de Stefano, S. (
1974
). Ajustement analytique des courbes de fécondité générale
. Population et Famille
, 32
, 53
–93
. 10.2307/1531801Farid, S. M. (
1973
). On the Pattern of Cohort Fertility
. Population Studies
, 27
, 159
–168
. 10.2307/2173460Gilje, E. (
1969
). Fitting Curves to Age-Specific Fertility Rates: Some Examples
. Statistical Review of the Swedish National Central Bureau of Statistics III
, 7
, 118
–134
.Hadwiger, H. (
1940
). Eine analytische Reprodutions-funktion für biologische Gesamtheiten
. Skandinavisk Aktuarietidskrift
, 23
, 101
–113
.Hansen, Hans Oluf. 1976. The Collecting and Compiling of Demographic Data to Assist in Policy Making, Planning, Public Administration and Demographic Research between 1950 and 1975. Pp. 5–17 in Proceedings of Northern Population Workshop I (Paula Weston Wells, ed.). The Arctic Institute of North America.
Hoem, Britta and Carsten Torpe. 1977. Regionale fertilitetsforskelle 1971-1976. Danmarks Statistik, Statistiske Undersøgelser #35.
Hoem, Jan M. (
1971
). On the Interpretation of the Maternity Function as a Probability Density
. Theoretical Population Biology
, 2
, 319
–327
. 10.1016/0040-5809(71)90023-2Hoem, Jan M. 1972. On the Statistical Theory of Analytic Graduation. Pp. 569–600 in Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability.
Hoem, Jan M. (
1976
). The Statistical Theory of Demographic Rates: A Review of Current Developments (with Discussion)
. Scandinavian Journal of Statistics
, 3
, 169
–185
.Hoem, Jan M. and Erling Berge. 1974. Theoretical and Empirical Results on the Analytic Graduation of Fertility Curves. Pp. 363-371 in Proceedings of the 8th International Biometrie Conference. Constanta, Romania.
Hoem, Jan M. 1975. Some Problems in Hadwiger Fertility Graduation. Scandinavian Actuarial Journal. Pp. 129–144.
Hoem, Jan M., & Holmbeck, Britta (
1975
). The Demographic Interpretation of the Basic Parameters in Hadwiger Fertility Graduation
. Statistical Review of the Swedish National Central Bureau of Statistics III
, 13
, 369
–375
.Hoem, Jan M. and Bo Rennermalm. 1978. On the Statistical Theory of Graduation by Splines. University of Copenhagen, Laboratory of Actuarial Mathematics, Working Paper No. 14.
Holmbeck, Britta. 1975. Fruktsamhetens regionala variationer 1968–1973. Swedish National Central Bureau of Statistics, Information i prognosfrågor 1975:2. (With a separately bound appendix of diagrams and tables.)
Jägers, Peter (
1974
). Convergence of General Branching Processes and Functionals Thereof
. Journal of Applied Probability
, 11
, 471
–478
. 10.2307/3212691Johnson, N. L., & Kotz, S. (
1970
). Continuous Univariate Distributions I
. Boston
: Houghton Mifflin
.McNeil, D. R., Trussell, T. J., & Turner, J. C. (
1977
). Spline Interpolation of Demographic Data
. Demography
, 14
, 245
–252
. 10.2307/2060581Mitra, S., & Romaniuk, A. (
1973
). Pearsonian Type I Curve and Its Fertility Potentials
. Demography
, 10
, 351
–365
. 10.2307/2060844Murphy, E. M., & Nagnur, D. N. (
1972
). A Gompertz Fit that Fits: Applications to Canadian Fertility Patterns
. Demography
, 9
, 35
–50
. 10.2307/2060544Rennermalm, Bo (
1978
). Utjämning av demografiska kvoter med kubiska splinefunktioner
. Statistical Review of the Swedish National Central Bureau of Statistics III
, 17
, 432
–438
.Rennermalm, Bo, & Arvidsson, Arne (
1977
). Utjämning av svenska fruktsamhetskurver 1968–1973 med kubiska splinefunktioner
. Statistical Review of the Swedish National Central Bureau of Statistics III
, 15
, 389
–401
.Rennermalm, Bo and Margit Strandberg. 1978. Regionala fruktsamhetstal för perioderna 1968–1970, 1971–1973, 1974–1976. Swedish National Central Bureau of Statistics, Information i prognosfrågor, preliminary version. (With a separately bound supplement of diagrams and tables.)
Retherford, Robert (
1979
). The Brass Fertility Polynomial
. Asian and Pacific Census Forum
, 5
, 15
–22
.Rogers, A., Raquillet, R., & Castro, L. J. (
1978
). Model Migration Schedules and Their Applications
. Environment and Planning A
, 10
, 475
–502
. 10.1068/a100475Romaniuk, A. (
1973
). A Three-Parameter Model for Birth Projections
. Population Studies
, 27
, 467
–478
. 10.2307/2173766Ross, G. J. S. (
1970
). The Efficient Use of Function Minimization in Non-Linear Maximum-Likelihood Estimation
. Applied Statistics
, 19
, 205
–221
. 10.2307/2346325Ross, G. J. S. 1974. Fitting Models to Ecological Data. Proceedings of the 8th International Biometrie Conference, Constanta, Romania.
Suchindran, C. M., Namboodiri, N. K., & West., K. K. (
1977
). Analysis of Fertility by Increment-Decrement Life Tables
. Proceedings of the Social Statistics Section, American Statistical Association
, 1
, 431
–436
.Woll, Claus A. 1978. Fertilitetsforskelle i København 1971–76. Københavns statistiske kontor, Undersøgelse No. 18.
Wunsch, G. (
1966
). Courbes de Gompertz et perspectives de fécondité
. Recherches Économiques de Louvain
, 6
, 457
–468
.Wunsch, G. (
1980
). Linéarisation de la fonction de fécon-dité générale par age
. Louvain
: Université Catholique
.Yntema, L. (
1969
). On Hadwiger's Fertility Function
. Statistical Review of the Swedish National Central Bureau of Statistics III
, 7
, 113
–117
.© Population Association of America 1981
1981
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