Journal of Population Research

, Volume 21, Issue 1, pp 95–98 | Cite as

Spline interpolation for demographic variables: The monotonicity problem

  • Len Smith
  • Rob J. Hyndman
  • Simon N. Wood


In demography, it is often necessary to obtain a monotonic interpolation of data. A solution to this problem is available using the Hyman filter for cubic splines. However, this does not seem to be well known amongst demographers, and no implementation of the procedure is readily available. We remedy these problems by outlining the relevant ideas here, and providing a function for the R language.


interpolation splines monotonic age groups age distribution deaths data bank 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Brown, H.P. and A.R. Hall. 1978.Australian Demographic Databank, Volume I: Recorded Vital Statistics 1921–1976. Volume II: Population Estimates and Demographic Rates 1921–1976. Canberra: Department of Economics, Research School of Social Sciences, The Australian National University.Google Scholar
  2. Dalgaard, P. 2002.Introductory Statistics with R.. New York: Springer.Google Scholar
  3. Dougherty, R.L., A. Edelman and J.M. Hyman. 1989. Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation.Mathematics of Computation 52: 471–494.CrossRefGoogle Scholar
  4. Hyman, J.M. 1983. Accurate monotonicity preserving cubic interpolation.SIAM Journal on Scientific Computing 4(4): 645–654.CrossRefGoogle Scholar
  5. Krishnamoorthy, S. and B. Derrick. 1983.Australian Demographic Databank, Volume III: Recorded Vital Statistics, Population Estimates and Demographic Rates 1976–1981. Canberra: Department of Demography, Research School of Social Sciences, The Australian National University.Google Scholar
  6. Maindonald, J. and J. Braun. 2003.Data Analysis and Graphics using R: An Example-based Approach. Cambridge: Cambridge University Press.Google Scholar
  7. McNeil, D.R., T.J. Trussell and J.C. Turner. 1977. Spline interpolation of demographic data.Demography 14(2): 245–252.CrossRefGoogle Scholar
  8. Wilmoth, J.R. 2002. Methods protocol for the human mortality database, revised 1 October 2002. 11 November 2003.Google Scholar

Copyright information

© Springer Science+Business Media 2004

Authors and Affiliations

  1. 1.Monash UniversityMelbourneAustralia
  2. 2.The University of GlasgowGlasgowUK
  3. 3.Australian Centre for Population ResearchThe Australian National UniversityAustralia

Personalised recommendations