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Generalizing Ripley's K function to inhomogeneous populations

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  • Eric Marcon

    (ECOFOG - Ecologie des forêts de Guyane - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - INRA - Institut National de la Recherche Agronomique - UAG - Université des Antilles et de la Guyane - AgroParisTech - CNRS - Centre National de la Recherche Scientifique)

  • Florence Puech

    (LET - Laboratoire d'économie des transports - UL2 - Université Lumière - Lyon 2 - ENTPE - École Nationale des Travaux Publics de l'État - CNRS - Centre National de la Recherche Scientifique)

Abstract

In spatial statistics, Ripley's K function (Ripley, 1977) is a classical tool to analyse spatial point patterns. Yet, it faces two major limits: it is only pertinent for homogeneous point processes and it does not allow the weighting of points.We generalize it to get a new function, M, which oversteps these limits and detects spatial structures of inhomogeneous populations of weighted points.

Suggested Citation

  • Eric Marcon & Florence Puech, 2009. "Generalizing Ripley's K function to inhomogeneous populations," Working Papers halshs-00372631, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00372631
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00372631
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    1. J. O. N. Perkins, 1977. "Comment," Economic Papers, The Economic Society of Australia, vol. 1(56), pages 35-35, October.
    2. J. P. Nieuwenhuysen, 1977. "Comment," Economic Papers, The Economic Society of Australia, vol. 1(53), pages 73-75, January.
    3. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    4. A Getis, 1984. "Interaction Modeling Using Second-Order Analysis," Environment and Planning A, , vol. 16(2), pages 173-183, February.
    5. Jones, Andrew P. & Langford, Ian H. & Bentham, Graham, 1996. "The application of K-function analysis to the geographical distribution of road traffic accident outcomes in Norfolk, England," Social Science & Medicine, Elsevier, vol. 42(6), pages 879-885, March.
    6. Gatrell, A. C. & Bailey, T. C., 1996. "Interactive spatial data analysis in medical geography," Social Science & Medicine, Elsevier, vol. 42(6), pages 843-855, March.
    7. Edward J. Feser & Stuart H. Sweeney, 2000. "A test for the coincident economic and spatial clustering of business enterprises," Journal of Geographical Systems, Springer, vol. 2(4), pages 349-373, December.
    8. S P Kingham & A C Gatrell & B Rowlingson, 1995. "Testing for Clustering of Health Events within a Geographical Information System Framework," Environment and Planning A, , vol. 27(5), pages 809-821, May.
    9. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
    10. J. H. K. Brunner, 1977. "Comment," Economic Papers, The Economic Society of Australia, vol. 1(56), pages 34-35, October.
    11. Eric Marcon & Florence Puech, 2003. "Evaluating the geographic concentration of industries using distance-based methods," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 409-428, October.
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